Dissertation

MEASURING LIQUIDITY RISK USING COMPOUND OPTION
Poonam Arvindbhai Thakker A4037197 i
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STATEMENT 1
This thesis is the result of my own investigations, except where otherwise stated. Where
correction services have been used, the extent and nature of the correction is clearly marked in a
footnote(s).
Other sources are acknowledged by footnotes giving explicit references. A bibliography is
appended.
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Poonam Arvindbhai Thakker A4037197 ii
Acknowledgment
I would like to acknowledge the assistance of my supervisor, Professor Dr. Andry
Rakotovololona for his great insights and perspectives guidance.
This dissertation would not have been possible without ideas, entailing suggestions,
encouragement, supervision and advices I had from my supervisor. His knowledge and
professional teaching style encouraged me to select the subject of my dissertation. It has been a
pleasure to work with him in this research and would like to thank him for all his support.
My sincere thanks go to all my professors, whose guidance helped me to learn and understand
the complex forms in finance and management throughout the course.
Lastly, I would like to thank my mother and my husband, who has been real inspiration to me.

Poonam Arvindbhai Thakker A4037197 iii
Abstract
Subprime crisis which lead to financial crisis of 2007 has been a great challenge for financial
world. Since this crisis has played big role in shaking the whole financial system, hence finding
the cause of this crisis and defining the solution has been main objective of financial institutions
and banking industry. Until 2007 Liquidity risk was not considered as one of the major risk by
management of most of the firms, although it was always the part of their risk component but
very low emphasis was placed on it. Many big financial institutions and banks fall in to default
or were in bail out position because of their irresponsible behavior towards their liquidity risk,
which further led to the credit risk exposure.
This research paper is an exclusive attempt of representing the integrated relationship between
liquidity risk and credit risk by using the Merton option (1974) and Geske compound option
theory (1977). The researcher is defining the liquidity risk as a compound option which led the
firm to credit risk exposure. The researcher has analyzed the Citigroup’s bailout which was
carried out by US government in 2008, to prove the validity and accuracy of the model in a
stochastic frame work. The researcher calculates liquidity coverage ratio for Citigroup to
analyze the result of her proposed option. The researcher gathers data stating the credit ratings
of Citigroup for the same time horizon to support her reasoning and to validate her proposed
compound option.
The researcher finds that it is possible to measure liquidity risk and credit risk using compound
option proposed by the researcher. Calculated compound option value goes higher when
Citigroup’s liquidity fund goes down and as Citigroup gets closer to its default point compound
option value goes higher on gradual basis. Liquidity coverage ratio and Finch credit rating
adopted by the researcher also supports the researcher’s proposal.

Poonam Arvindbhai Thakker A4037197 iv
TABLE OF CONTENT
CHAPTER: 1 – INTRODUCTION........................................................................................... 1
1.1 RESEARCH QUESTIONS:....................................................................................................... 2
1.2 RESEARCH OBJECTIVES: ..................................................................................................... 2
CHAPTER: 2 - LITERATURE REVIEW ............................................................................... 3
2.1 - LIQUIDITY RISK:................................................................................................................ 3
2.2 - LOAN PRICING:.................................................................................................................. 7
2.3 - DEPOSIT INSURANCE:........................................................................................................ 7
2.4 - BASEL III:......................................................................................................................... 10
2.5 - COMPOUND OPTIONS:..................................................................................................... 11
2.6 - RESEARCH GAP:.............................................................................................................. 13
CHAPTER: 3 - RESEARCH METHODOLOGY ................................................................. 15
3.1 INTRODUCTION:................................................................................................................. 15
3.2 RESEARCH OBJECTIVES: ................................................................................................... 15
3.3 METHODOLOGY AND DESIGN OF THE RESEARCH:............................................................. 15
3.3.1 Research Philosophies:.............................................................................................. 15
3.3.2 Research philosophy implemented:............................................................................ 16
3.4 RESEARCH APPROACHES:.................................................................................................. 17
3.4.1 Research approach chosen:....................................................................................... 17
3.5 RESEARCH STRATEGIES:.................................................................................................... 17
3.5.1 Research strategies employed:................................................................................... 19
3.6 TIME HORIZONS:................................................................................................................ 19
3.7 RESEARCH CHOICE OF TECHNIQUES AND PROCEDURES:................................................... 19
3.7.1 Data sources:............................................................................................................. 19
3.7.1 (A) Implementation of sources: ............................................................................. 20
3.7.2 Bench marks: ............................................................................................................. 20
3.7.2(A) Benchmark used for this research:.................................................................... 20
3.8.1 Research choice implemented:................................................................................... 21
3.9 ETHICS AND CORPORATE GOVERNANCE: ......................................................................... 22
3.10 RESEARCH METHODOLOGY IMPLEMENTED:.................................................................... 22
3.10.1 Theories used for the research: ............................................................................... 22
3.10.1(A) Merton’s call option ....................................................................................... 23
3.10.1(B) Geske’s compound option (1977)................................................................... 24
3.10.1(C) Maltritz model (2009)..................................................................................... 24

Poonam Arvindbhai Thakker A4037197 v
3.10.1(D) Hui-Lo valuation model (2000)...................................................................... 24
3.10.2 Proposed compound option by researcher: ............................................................. 24
3.10.3 Comparison with Basel 3 ratio:............................................................................... 25
3.10.4 Bench mark implementation: ................................................................................... 27
CHAPTER: 4 – RESEARCH ANALYSES ............................................................................ 28
4.1 PROPOSED COMPOUND OPTION......................................................................................... 28
4.2 LIQUIDITY COVERAGE RATIO ........................................................................................... 33
4.3 CREDIT RATING................................................................................................................. 35
CHAPTER: 5 - CONCLUSION AND RECOMMENDATION........................................... 38
APPENDICES........................................................................................................................... 40
APPENDIX - (A) ....................................................................................................................... 40
APPENDIX - (B)........................................................................................................................ 41
APPENDIX - (C)........................................................................................................................ 57
APPENDIX - (D) ....................................................................................................................... 58
APPENDIX - (E)........................................................................................................................ 61
REFERENCES.......................................................................................................................... 63

Poonam Arvindbhai Thakker A4037197 1
CHAPTER: 1 – INTRODUCTION
Global financial market has long history of fighting against different types of crisis. Different
crisis have different characteristics and has variable effects on market. Some of them have
turned in to global crisis due to their intense nature. Innovations and electronic communication
developments has bought global financial world within close proximity and thus they highly
rely on each other. Due to these, crisis has even deeper and bigger impact on financial markets
and certainly is not limited to geographical location. Currency crash, Currency debasement,
Inflation, banking crisis, Sovereign crises, debt crises and sub-prime crises are few examples
from which we can learn from and avoid exposure to them.
During late 2007 United States was the first country to hit by recession. This was due to decline
in real estates which was previously considered as the most recession proof area of investment.
Due to low risk attached to securities, financial institutions and Banks developed derivatives
such as CDOs (Collateralized debt Obligation) and MBS (Mortgage Based Securities) which
were used for hedging purposes to reduce the exposure and increase the liquidity (Triana, 2009).
Collateralized debt obligations are special purpose vehicle collecting cash against a portfolio of
fixed income assets such as commercial loans (Hull 2007). These CDO’s were issued in return
of cash according to the rating given to them such as AAA which are superior to BB which are
inferior and lastly without ratings. In order to improve their rating to increase the salability of
these CDO’s banks started mixing them with MBS. Hull (2007) has explained Mortgage based
securities as ‘a type of asset-backed security that is secured by a mortgage or collection of
mortgages. These securities must also be grouped in one of the top two ratings as determined by
an accredited credit rating agency, and usually pay periodic payments that are similar to coupon
payments. Furthermore, the mortgage must have originated from a regulated and authorized
financial institution’. As such derivatives were considered having low risk, heavy emphasis was
put on such instruments and was traded heavily in the worldwide markets. Financial institutions
started to create more complex structured products (CDOs of ABS) to obtain higher ratings.
Because these instruments are mixed bundles of secured and unsecured obligations, they were
able to reduce their risk exposure. Strong model risk had heavy dependency on the underlying
models. Standard models have failed to quantify risk in CDOs of ABS (Asset based Securities).
As it was general failure to capture systemic contagion and high default correlation regime. In
early 2007 financial market started showing the effects of crisis. Schwartz (2009) in his article
explains that adoption of innovations in investment instruments like securitization, derivatives
and auction-rate securities influenced the emergence of credit crisis. Most of the financial
institutions were bankrupted or bailed out by government or merged during the crisis. The

biggest example was Lehman Brothers the 4th
largest investment bank collapsed in 2008, the
largest bankruptcy in history with $ 639 billion in assets and $619 billion in debt (Financial
Times, 2009). Bear Stearns and Merrill Lunch were taken by other companies, while Goldman
Sachs and Morgan Stanley and Citigroup were bailed out by government. Investment banks and
financial firms caused panic in financial market and investors (depositors) were encouraged to
withdraw their money out of market. These led to liquidity problems in financial markets as
banks and financial institutions did not have enough liquidity to fulfill their short terms
liabilities as their major source of liquidity was depositors.
Major cause of 2007 financial crisis was due to financial institutions nature to carry high level
of liquidity risk exposure, which ultimately led many financial institutions closer to default risk
or credit risk as seen some examples earlier. Finding the Solution of this crisis became biggest
challenge for financial world. As crisis wasn’t just limited to any particular institution or
particular country the main objective was to make sound banking system worldwide. Many
attempts have been made worldwide to find the real cause and to offer the solution.
In this paper the researcher is attempting to offer the way banks can measure their liquidity risk
exposure which can lead to distance to default (credit risk) using the compound option firstly
suggested by Merton (1977) and then updated by Geske (1974). This will help any bank or
company to find their liquidity position and also will highlight how far their liquidity position is
from their default point.
1.1 Research Questions:
Q - Is liquidity risk a double option integrating credit risk in Merton and Geske terms?
Q - Does liquidity risk have direct impact on company’s credit risk exposure?
1.2 Research Objectives:
 To identify the relationship between liquidity risk and credit risk.
 To estimate liquidity risk and credit risk exposure of the company using compound
option.
 To evaluate default position (caused by liquidity) for particular company using
compound option is possible.

CHAPTER: 2 - LITERATURE REVIEW
This research is carried out after careful study of the various literature focused around the
proposal. There has been an in-depth analysis and review carried out on Compounded options,
Liquidity risk and Deposit insurances as they are main components of my research topics. Sub-
prime crisis has led to detailed research in to these areas which has mentioned below.
2.1 - Liquidity risk:
Here we can define liquidity as the ability of a financial firm to meet its debt obligations without
incurring unacceptably large losses. Thus Liquidity risk is the risk that a firm will not be able to
meet its current and future cash flows and collateral needs, both expected and unexpected,
without materially affecting its daily operations or overall financial condition (FRBSF 2008).
Recent financial crisis has focused attention towards the liquidity risks faced by the financial
institutions and banks. BASEL 3 regulations is enacted exclusively to focus on the liquidity
issues faced by the banks. Many writers have tried to focus on these issues and are shown
below.
Berger and Bouwman (2010) have raised the liquidity issue in their paper and have focused on
how banks react on normal times and during crisis. They have used virtually all U.S. banks data
from 1984 to 2008 quarter four to formulate a hypothesis to address their questions. Their
findings suggest that monetary policy does not affect liquidity creation by large and medium
bank. Monetary policy’s effect on liquidity creation is much weaker during crisis than normal
time and also liquidity creation tends to be high prior to financial crises. However, their research
does not incorporate the study of credit risk.
Ganga and Trevisan (2010) also have tried to review the solution for liquidity risk in their
literature by analyzing trends before and after 2007 financial crisis. They have provided an
overall review of CEBS’s (Committee of European Banking Supervision) proposals to fix the
criteria for quantitative and qualitative definition of the liquidity buffer and they have proposed
few considerations to improve the regulation for liquidity risk. They also suggest that there is
tight correlation and interdependence between liquidity risk and other types of banking related
risk.
Comett, McNutt, Strahan and Tehranian (2010) have analyzed the bank’s behavior during 2007-
2009 financial crises and how they adjusted their holdings to create liquidity. As banks that used
equity and core deposit for their finance carried on lending to other banks while banks with
more illiquid assets increased asset liquidity and reduced lending and as result it displaced the
overall lending capacity. Their empirical study confirmed that in effort to manage the liquidity
crisis, banks led to a decline in credit supply. However, it does not provide enough evidence that
correlates liquidity risk directly to credit risk.

Denecker, Kapoor and Noteboom (2010) have discussed, how liquidity risk should be measured
after suffering from recent 2007 crisis and also suggesting the frame work to manage liquidity
risk. In their frame work liquidity has four different faces, Transactional liquidity risk, market
liquidity risk, tradability risk and long term funding risk which happens in the sequence and
follow the cycle. According to their frame work, there are four approaches should be focused to
manage liquidity risk, Methodology, Metrics and tools, Operations and execution, Strategy and
governance. Their study is related more towards corporate governance compared to risk
management and lacks link between different types of risks.
Chu (2007) in his article declares that standard & Poor’s has changed the way they use to assess
the liquidity risk profile of Canadian banks. They have also adopted new Canadian liquidity
model to measure the banks performance under liquidity crisis. He also discuss that their new
model consist the “run on bank” scenario to enhance their measurement. This paper also
highlights the benefits of regulatory oversight and system support to the ratings on the Canadian
banks. But his research has geographical limitations which are based on concentrated study.
Praet and Herzberg (2008) in their article discuss the issues related to market liquidity and
banking liquidity, vulnerabilities and the role of disclosure. Their studies have focused on
European bank’s data to find and discuss the issue. They represent how banks have become
more vulnerable to market liquidity shocks, the mechanics behind bank’s market-banking
liquidity relationship during stress market, market liquidity crisis and its implications for
liquidity in the whole banking sector. Their article also highlight on benefits of disclosure as
financial institutions will not have to be victim of misinformation and also it will bring a
necessary discipline on bank’s transparency. But, it does not propose the model to calculate
those risks.
Carletti, Allen and Gale (2011) have developed a model in which suggests that fiat money has to
be issued by central bank as per requirement of private sector and these money should be used
as unit of account and also as a medium of exchange. According to their new model, with
nominal contracts by central bank it is possible to eliminate financial instability. This will allow
the central bank to accommodate the commercial bank’s liquidity needs. As central bank can set
the nominal interest rate, they also will be able to control the expected rate of inflation. Their
model however focuses more on the liquidity issues faced by respective governments and does
not provide solution for liquidity risk issues for financial institutions.
Wagnall and Atkinson (2010) discuss the Basel 3 proposal and its structured elements with its
benefits and some issues. They highlight some key elements of Basel 3which are very useful to
cover liquidity of the bank such as, leverage ratio, a capital buffer etc. In their analyses they
have compared Basel 3 proposal with Basel 1 and 2 by using different models like IRB
approach. They have also raised some concerns in their paper about Basel 3. They suggest that
Basel 3 needs to address the regulatory problem that the “promises” that make up financial

system are not treated equally. Another concern is that whether the shadow banking system
should be incorporated in to regulatory frame work.
Alquist (2008) in his paper has mentioned importance of liquidity risk by defining the
relationship between market liquidity risk and sovereign bond risk premium. He has used
London Stock Exchange bond prices data during 19th
century. He has used two asset pricing
models that formalize the relationship between expected returns and liquidity risk. One is from
(Achrya and Pedersen 2005) and second one is (Bekaert et al 2007). His Empirical analysis of
these data establishes two results. One is illiquid sovereign bonds carry larger factor loadings on
fluctuations in market liquidity relative to more liquid sovereign bonds. Their results suggest
that investors value a bond's liquidity and avoid holdings illiquid bonds when market liquidity
dries up. And secondly, liquidity risk is important for pricing sovereign debt. This results still
does not provide the possible model which can be used for future analysis.
Baglioni in his paper has tried to analyze that the liquidity crunch in the intra-bank market was
due to liquidity risk or credit risk. In 2010, His analysis proves the impact of bad news affecting
the market in the future bears important consequences or the intra-bank. Market participants
belief can led to gridlock. Their demand goes up for liquidity premium for lending maturities
longer then short ones. They did proved relationship between liquidity risk and credit risk faced
by these banks but no measurement model is suggested.
Bali and Cakici (2009) in their paper investigates that world market risk, country specific total
risk and idiosyncratic risk are priced in International capital asset pricing model (ICAPM). They
also tries to investigate and proposed that differences in countries stock market returns can be
defined by differences in systematic and country specific risk. They have taken sample of 23
developed and 14 emerging market for a total of 37 countries. They have used hypotheses to
prove that theory and their hypotheses rejects that country specific total and idiosyncratic risks
are not priced and they also suggested that the prices of risks associated with the relevant factors
are not the same across countries.
Banti and Phylakits (2011) in their paper also try to analysis the liquidity risk involved in
foreign exchange market. They tried to find whether liquidity risk is priced in the cross section
of currency returns and tries to find estimation for liquidity risk premium in the foreign
exchange market. To support their study they use data comprising daily order flow for 20
exchange rates for 14 year. Their empirical study suggests that the magnitude of liquidity of the
risk premium increased substantially after the collapse of Lehman Brothers in financial crisis.
Their study included review of short term liquid assets, but was not connected to credit risk.
Norden and Wagner (2008) examine the relationship between credit default swaps and loan
pricing. They use baseline model for their empirical study. Their model suggests that CDS are
strongly linked to spreads on new syndicated loans. Their study is also proving that Credit
Default Swaps (CDS) has influence on loan rates.

Lee (2006) has tested Acharya and Petersen’s Liquidity adjusted capital asset pricing model by
extending it to global level. He has used data from 50 different countries from 1988 to 2007. His
study suggests that worlds price of liquidity risk is more important than the local areas.
According to his model the liquidity risks are priced independently from the market risk in
international markets.
Beirne, Caporale and Spagnolo (2010) have modeled volatility of the spread between the
overnight interest rate and the central bank policy rate during financial crisis. They have focused
on EU and UK area for their studies. They used stochastic volatility models to find the role
played by liquidity risk and credit risk causing the spread between the overnight interest rate
and the central bank policy rate during financial crisis. They shows in their results that liquidity
risk is the main component of the volatility of the policy spread but they also suggests that
excessive volatility in the spread can damage the monetary policy in the market. The main
policy implication of their analysis would be the control of the volatility in the policy spread.
Drehmann and Nikolaou (2010) in their paper have proposed the measure of funding liquidity
risk. They suggested that we can extract an insurance premium from bank's bids to fund
liquidity risk. To conduct their study they have gathered data from 170 main refinancing
operation auctions between June 2005 and December 2007 in Euro area. They show in their
research that funding liquidity risk increased rapidly after August 2007. They suggest that there
is inverse relationship between finding liquidity risk and market liquidity.
Anson (2010) in his article explains liquidity risk from investor’s point of view that it is the risk
that investor will not be able to sell his/her assets in timely manner or it can only be sold at
discounted value. He offers a frame work to measure liquidity risk and calculations to arrange
the premium for that risk. In his point of view assets portfolio should be divided in to four large
risk buckets instead of allocating them in to traditional asset classes for example, fix income
bucket to be Liquidity Bridge to fund the less liquid bucket of real estate. He suggest that
quantification of liquidity risk is very difficult task but institutional investors has started
adopting polices which reflects this risk.
Prefontaine, Desorchers and Godbout from University of Sherbrooke in their Economic
research journal (2010) has shared their analysis with Basel Committee on Banking Supervision
(BCBS) and it leads to conclusion of full support to the adoption of the BCBS proposals on two
new liquidity risk management standards, the Liquidity coverage ratio and net stable funding
ratio both to be accompanied by a mandatory set of market related monitoring tools. They have
also came across with some suggestions like the need to formulate and implement more precise
liquidity risk requirements on foreign currency funding, the importance and usefulness of
enhancing liquidity risk public financial disclosure, extending the use of real sector and market
related monitoring rules and metrics. They also added specific comments and suggestion about
needs to work on intra group and cross border foreign currency liquidity risk management,

clarifying the definitions of liquidity coverage ratio and net stable funding ratios, defining
required stable funding categories. Their paper concludes with the importance of enhanced
capital structure requirements for banks. Their suggestions also lead to more considerations and
also discuss some gaps in their new structures needs to be worked on. Similar study is
performed in this paper which evaluates proposed compound option.
2.2 - Loan Pricing:
Bordo and Rousseau (2011) have developed study about the relationship between financial
developments, international trade and growth. They have taken their sample from 17 countries
from 1880 to 2004. Their study is based on cross –country growth regression frame work. Their
empirical study suggests that trade has its strong effects after 1945 and later it expanded by
establishment of World Trade Organization in 1995. While, financial development and growth
has positive relationship thorough the time line which they chosen as sample. They also support
the judgment that well established and deep financial sector and sound trading arrangements
have its positive effects on long term growth.
Calabrese and Zenga (2008) in their paper have attempted to develop new methodology for
recovery percentage calculation. They have adopted Monte Carlo simulations process. They
have taken Bank of Italy as their sample. They present the parametric model, the combination of
a right – skewed and symmetric random variables for recovery rate calculation.
Khieu et al (2011) have employed the model to analyze bank loan recovery rate considering
loan and borrower’s characteristics and some other variables. They have taken Moody’s
Ultimate Recovery Database from 1987 to 2007. This empirical study suggests that loan
characteristics are more significant than borrower’s characteristics before default situation as
determinants of recovery rate. They also suggest that there is correlation between 30 day post
default trading prices and settlement recoveries.
Louzis et al (2010) have analyzed the determinants of non-performing loans and they have
compared the different determinant’s performance to each other to get the result. They have
adopted dynamic panel data methods to examine their study. They have taken Greek banking
sector as their sample. Their empirical analyses suggests that GDP growth rate, unemployment
rate, public debt have influence on the level of non-performing loans.
2.3 - Deposit insurance:
Deposit insurance is a step taken by many countries to protect the money of short term deposits
made by common public. This system provides guarantee to depositors either in full or part.

Banks ideally lends most of the money they have and if the borrower has defaulted, bank will
not be able recover those money and will not be able to pay back to their depositors. Merton
(1977) initially tried to derive formula for cost of deposit insurance and loan guarantee. Similar
research paper was followed by Black and Scholes (1973) who emphasized that Merton’s
definition of option value of deposit insurance was unclear in two ways. According to Merton
option value of deposit insurance is actually component of the shareholder’s limited liability
option under a third party deposit guarantee.
Merton (1977) has defined the derivation of the cost of deposit insurance. Third party guarantee
is not a new approach rather it has been adopted in corporate since century. In insurance when
third party becomes a guarantor they are liable to the cost or a liability to their guarantee.
Merton had derived the formula in his paper determining these costs. He has used option pricing
theory to support his research. He has developed his model adopts put option theory. There is
some disapproval to this theory which the researcher will discuss next.
There have been some challenges to Merton approach by Fegatelli (2009). He has been brave in
his paper in 2007 which revised in 2009 by challenging Merton’s work which was also followed
by Keeley and Furlong (1990). The concepts are different but strictly related and these study re-
asses the M (Merton) model. As M model didn’t define who will be benefiting from a third
party deposit insurance guarantee. Fegatelli’s hypotheses suggests that Bank’s capital is a call
option on the bank’s assets at strike price equal to the value of the bank’s liabilities (Merton
approach) and as the option value of deposit insurance was already in the call option it cannot
be added later in the formula again.
Duffie et al (2003) proposed empirical method of market valuation of deposit insurance which
is based on reduced form methods for pricing of fixed income securities under default risk. They
have treated banks without public debt pricing by extending conventional reduced form
methods for the pricing of fixed income securities under default risk and then they have applied
valuation model to calculation of fair market deposit insurance premia (Premium) and to
valuation of long term claims against the insurer. They have reviewed standard deposit
insurance contracts provided by the United States Federal Deposit Insurance Corporation
(FDIC). They suggests in their study that risk neutral valuation model for deposit insurance can
be applied both to the calculation of fair market deposit insurance permia and to the valuation of
long term claims against the insurer.
Sheehan (2010) has proved in his paper by employing bank specific data on core deposits that
they have higher value to financial institutions even more than regulators have allowed. He has
used conceptual model for his estimation and he considered both a base case interest rate
scenario and alternate interest rate scenario based on the standard Asset – Liability management
approach used by both regulators and financial institutions. He has used five banks as a
representative for his application as limitation of having enough data.

Vallascas et al (2009) have proposed a new approach for the estimation of the loss distribution
of deposit insurance scheme which was based on Basel 2 frame work. They adopted the
distribution of bank’s losses based on Basel 2 framework and concentrate the part of losses
which was not covered by capital. They have taken Italian bank’s data from 2007 to implement
their new approach. They also take in to account the correlation between bank’s assets and
interbank lending contagion. They conclude in their approach that policy makers should cover
the regulatory frame work which banks follows and also correlation of bank’s assets and the risk
of interbank contagion as it is not possible to assess the deposit insurance system in bad market
condition with significant amount of contagion between banks.
Hakenes and Schnabel (2008) have analyzed the effects of banks competition on their capital
requirements on financial stability. They introduce bank equity and capital regulations when the
relationship between banking competition and stability is ambiguous in nature. Then they
review the impact of capital requirements on bank’s correlation, risk attached with each loans
and probability of default. Their results suggest that capital regulation could be the cause of
destabilized banking system due to effect on banking competition.
Hardin et al (2009) have analyzed the impacts of capital requirements, deposit insurance and
franchise value on the bank’s capital structure. Their analyses suggest that bank’s optimal
capital structure relay on deposit based bank’s franchise value. Their empirical model shows
that optimal market leverage increases when value of the franchise declines.
Madan and Pennacchi (2003) in their conference paper have raised the issue on pricing the risks
of deposit insurance. They suggest that if banks are charging higher interest rates to its
borrowers, they tend to have higher average interest rate spread and could lead to greater
possibility of achieving poor loan performance. They argue that accounting ratios, ratings, loan
rate spread are more reliable signal of bank risk.
Morrison and White (2010) have developed new approach for provision of deposit insurance.
They have adopted stripped down model in which bankers are monitoring their investments for
improvement in their productivity and when it is subject to moral hazard their model set up that
deposit insurance constitutes a net subsidy to a banking system.
Sawada (2008) in his paper analyses the impact of liquidity shocks generated by depositor’s
behavior on bank portfolio management during financial crisis in a system lacking deposit
insurance. They discovered that banks reacted to liquidity shocks sensitively by increasing
liquidity through sale of securities in financial markets. However, this analysis was inconclusive
as there was insufficient evidence supporting the argument that the existence of the LLR
(Lender of last resort) mitigated the liquidity constraints in banking adjustments of liquidity in
bank portfolio in a system without deposit insurance schemes. However, this research takes step
further to analyze the point at which the LLR i.e. central bank will or should bailout. All other

researches in these areas have not been in close relation to what researcher is willing to suggest
here.
2.4 - Basel iii:
Basel committee was established by the central bank governors of ten countries in 1974. This
committee introduces Basel Capital Accord for capital measurement in 1988. The main
objective was to implement credit risk measurement frame work with minimum capital standard
of 8%by end of 1992. They kept revising the capital frame work according to the financial
market. Last it was revised after 2008 financial crisis to address the problems of the crisis which
has been introduced as BASEL iii (Basel committee, 2009). In Basel iii they have focused on
liquidity standard along with global capital standard as liquidity has played important role in
leading the 2007 financial crisis. The committee has used three different ratios to regulate the
liquidity among the banking sectors. First is Liquidity Coverage ratio which focuses on
resilience of liquidity disruptions over thirty day period. It will help ensuring that global banks
will have sufficient and high quality liquid assets to offset the net cash flows under short term
stress scenario. Second is Net Stable Funding Ratio which sets the requirements of minimum
amount of stable sources of funding at a bank relative to the liquidity profiles of the assets and
also to fulfill contingent liquidity needs arising from off balance sheet commitments over the
one year period. It also focus to control over reliance on short term wholesale funding during
times of lighter market liquidity and drives towards better assessment of liquidity risk across all
on and off balance sheet items (Basel committee 2010). Third is monitoring tools which
establish a set of common metrics to considered as the minimum types of information which
supervisor should use and they also can use additional metrics in order to capture specific risks
in their jurisdictions which includes (a) Contractual maturity mismatch (b) Concentration of
funding (c) Available unencumbered assets (d) LCR by currency (e) Market related monitoring
tools.
Basel committee (2011) has released this article providing detailed regulatory frame work in
Basel 3. This article states the main objectives of Basel 3, introduces the new liquidity standard
to be followed by banks, explains the different elements of capital requirements and it also
consist of information on capital conservation buffer, countercyclical buffer, leverage ratio.
Basel committee (2010) has issue the article about liquidity measurement, its standard and
monitoring. It elaborates on Basel 3’s regulatory standard, monitoring tools and issues concern
with its application. In regulatory standards it explains the definition of liquidity coverage ratio,
net stable funding ratio and its standards. In monitoring tools, the article explain contractual

maturity mismatch, concentrating of funding, available unencumbered assets and also market
related monitoring tools.
Basel committee (2010) has issued consultative document stating how Basel 3 will be useful for
strengthening the resilience of the banking sector. This document focuses on improvement of
banking sector’s ability to survive the shocks arise from financial and economic stress like 2007
financial crisis. Other areas Basel committee has also covered are to improve risk management,
more awareness in governance and bank’s transparency and disclosure policy. After reviewing
the causes of financial crisis Basel committee has also declared the key elements in their 6th
September 2009 meeting regarding the Basel 3 proposal. Which covers the all possible risk
factors can be affecting the banking sector.
2.5 - Compound Options:
Credit risk assessment plays very important role in financial world. Different types of crisis in
past has forced financial regulators to concentrate and devote more resources to this task.
Compound option has been considered very often for credit risk assessment. Firstly by Merton
(1974) followed by Geske (1977) which was revised again in 1979 then by Selby & Hodges
(1987) and Rubinstein (1991).
Merton (1974) has tried to assess credit risk of a company by treating Equity as value of a
levered firm is equivalent to call option on the value of the firm’s assets and strike price will be
the face value of the debt owed. The model assumes that a company has a zero coupon debt
which will be due a time T and equity receives no dividend. The company will default if its
assets value will be less than the promised debt payment at time T. The equity of the company is
a European call option on assets of the company with maturity time T. and strike price will be
equal to the face value of the debt. This model helps estimating risk natural probability of
default of the company. It can also be useful for measuring credit spread on the debt. This
option theory is considered as the based theory in this research.
Robert Geske was the first one after Merton, to expand compounded options. He has expanded
the Merton frame work by including multi period debt payment instead of single period. Geske
also suggests that variance rate of return is not constant as stated by Black – Scholes model but
it depends on the level of the stock price or on the value of the firm. Geske in his paper derives
new formula for the value of a call option as compound option which reflects leverage effects in
to Put – call option pricing. There has been more research carried out in this area which is
explained briefly in this paper.
Chan-Lau and Santos (2010) has developed Assets and Liability Management (ALM)
compound option model. Their model analyses and evaluates the risk profile of public debt

considering multi-period setting. To prove their theory they have analyzed the risk profile and
sustainability of G-20 countries’ public debt under different polices as illustration. Their model
is based on option pricing model developed by Geske (1977). The basic idea was that the value
of public sector net worth in a multi-period setting is equal to the value of compounded option
on the total assets which government holds. It is solved numerically by using the Least Squares
Monte Carlo (LSMC) simulation method. ALM compound option model can be used to identify,
monitor and control the risks associated with different fiscal policy and also to assess whether
the asset growth rate associated with primary surplus is consistent with asset and liability
matching needs.
Compound option-based structural credit risk model has been used to estimate the banking crisis
by Eichler, Karmann and Maltritz (2010). Their theory has provided separate information on
short term, long term and total crisis risk. They have tried to expand their theory from single
maturity risk measurement (Merton) by providing separate measure for short-term, long-term
and total crisis risk. They derived model from Duan’s (1994) maximum likelihood approach.
They have estimated total increasing crisis risk from July 2007 onwards because of short term
crisis risk. Based on their approach it is possible to determine separate default probabilities for
short term and long term maturity compare to total probability to default. Compare to Chan-Lau
and Santos where they determine distance to default, this approach additionally determines
short- term and long-term distance to default.
Gukhal (2003) in his paper proves against the assumptions from previous studies on compound
options that value of assets evolves as continues process. He has used compound option
approach to value American call options on stocks that pay discrete dividends and also
American option on assets that pay continuous proportional dividends. His paper derives an
analytical formula for compound options that the underlying asset follows a jump diffusion
process and then applies the result to value extendible options. However it does not show
relationship between liquidity and credit risks within their option.
Yu-Lin Huang and Chia-Chi Pi (2011) has bought new concept in their theory using
compounded option. They developed European sequential compound call option pricing model
concept for multistage investments with voluntary expansion. Investing in one area gives the
concessionaire an option to invest in the next area. The concessionaire will invest in the next
area only if that area’s underlying asset value exceeds a critical level. They adopt Black and
Scholes stochastic differential equation for underlying assets value of investment. This theory
supports the practice of facilitating multistage investment by granting exclusivity, expansion and
abandonment rights. It can be helpful to reduce the cost of capital. LIU (2008) came up with
compounded option formula that can be used for real project investments with underlying assets
being non-tradable. Geske’s (1979) compounded options formula had a drawback that it had
problem with evaluating underlying assets value when they are non-tradable as their market

value cannot be defined. Liu has implied two new compound option pricing formulas for
underlying non tradable assets. He has used good deal bounds method by Cochrane and Saa-
Requejo and others based on utility indifference approach derived in Henderson. Their study
was restricted to non-tradable assets while researcher is trying to analyze the value of compound
option using highly liquid or tradable assets.
Hui and Lo (2002) is presenting the valuation model of defaultable bond values in emerging
markets. They define default occurrence situation quiet different than what Merton (1974) and
Geske (1977) as we seen earlier. Their paper suggests that “the firm defaults when some
signaling process hits a pre- defined default barrier”. They adopted so called middle ground
model a mixture of structural models and the reduced form models of price defaultable bonds.
The signaling variables considered to be a foreign exchange rates. In their point of view
volatility of defined signaling variables (foreign exchange rate) affects the level of the default
barrier over the time, therefor it is more realistic to measure the default bond valuation rather
than by asset value of the firm like Merton (1977) approach.
Maltritz (2009) has done very interesting research and his paper is very close to what I would
like to conclude in my research. He has taken Hungarian financial crisis of 2008 in to
consideration for his research. His model analyses the dependency between financial crisis and
sovereign debt using a stochastic frame work and a compound option approach. It also advances
structural credit risk models for country default. With the help of structural approach estimates
can be made for the funds a country is able to and is willing to spend for debt services.
Structural credit risk has been also used to analyze crisis risk in banking sector. He has adopted
a structural model based on the compound option approach derived by Geske (1977). He
considers both problems banking sector and country default to gather as often they occur at the
same time. He captures them in one model which requires expanding the single payment frame
work like Chan- Lau and O has done in his paper. His frame work also helps to consider short
term and long term service payments separately. His analysis shows that a problem in domestic
banking sector does influence the total crisis risk as required bail out payments are relatively
low compared to debt services payments and short term risk rises dramatically compare to long
term during crisis in 2008.
2.6 - Research Gap:
As mentioned above in literature review, there have been many attempts to identify the causes,
to find the solutions and suggestions from different authors and researchers regarding exposure
to liquidity risk, distance to default and compound options. But there hasn’t been any discussion
or suggestion from any author or researcher proposing integrated relationship between liquidity

risk and credit risk using compound option. Based on Merton and Geske’s compound option
theory the researcher is trying to extend their compound model and to derive the formula to
measure liquidity risk and credit risk exposure. Basel committee has identified the importance
of liquidity and enacted the new regulation Basel 3 which focuses on the higher liquidity ratios.
However there has been no attempt made by them to integrate the liquidity and credit risk. Here,
the researcher’s idea is to recommend a framework and an option which can be used to evaluate
the bailout price of the company. This will be done by reclassifying the variables used by Geske
(1977) in his compound option formula.

CHAPTER: 3 - RESEARCH METHODOLOGY
3.1 Introduction:
Here, in this chapter the researcher will discuss main objectives of the research, design and
methodology used for research and philosophy implemented to carry out this research. The
researcher will present organized structure of the research with explanation of different
determinants used to answer the research question.
3.2 Research Objectives:
 To identify the relationship between liquidity risk and credit risk.
 To estimate liquidity risk and credit risk exposure of the company using compound option.
 To evaluate default position (caused by liquidity) for particular company using compound
option is possible.
3.3 Methodology and design of the research:
This section explains the methodology and structure used to carry out this research. It includes
research philosophy, research approach, research strategies.
3.3.1 Research Philosophies:
Research philosophy describes the development of the knowledge and the nature of the
knowledge or in other words developing new knowledge in particular field (Saunders et al,
2007). There are different types of research philosophies the researcher can choose from,
depending on types of research they carrying, the research question, aims and objectives of the
research. In management research there are three major ways to adopt research philosophy:
Epistemology, Ontology and Axiology. They all are different in nature and will have influence
the way researcher will carry out the research (Saunders et al, 2007).
Epistemology refers to what is acceptable knowledge in the particular field for research.
Positivism focuses on collection and analysis of facts. Researcher (like Natural scientists) who
follows positivism will consider reality which can be seen measured and modified for their
research. Researcher would be able to use this data to present in the form of table of statistical
data where it represents objectivity in researcher’s view. Researcher may also develop
hypothesis by using the existing theory. Most of the time positivist uses large sample to prove
their theory and adopts quantitative methods, however the researcher can also use the qualitative
methods. Realism is another part of epistemological position which is very much similar to
positivism as they both adopts the scientific approach for their research, but realism as the word

stated is a reality an independent thought of the mind. In realism the researcher’s beliefs can
have influence and can represent bias views in their research. There are two different forms of
realism direct realism and critical realism. Direct realism explains that what you can actually see
that is exactly what you can remember. On the other hand critical realism explains the illusion in
our mind, what we experience is sensation, the images of the things of the real world but not the
direct real world (Saunders et al, 2007). They both are important for business. Interpretivism is
an epistemology which explains that it is necessary for the researcher to understand differences
between humans in our role as social actors (Saunders et al, 2007). It is highly appropriate in
terms of organizational behavior, marketing and human resources.
Ontology is concerned with nature of reality. It considers both objectivism and subjectivism,
which we discussed in epistemology. Objectivism portrays the position that human accepts in
the social world. As example manager defines your job descriptions which will define your role
and responsibility as social actor. While subjectivism defines that social phenomena are created
from the perceptions and consequent actions of social actors. Pragmatism refers that most
important determinant of research philosophy adopted is the research questions. When
researcher adopts positivity and interpretivist philosophy which is perfectly fine for particular
research it defines as pragmatism (Saunders et al, 2007).
Axiology is one part of philosophy that studies judgments about value (Saunders et al, 2007). It
studies the researcher’s view on the roles played by values in all stages of the research process.
A statement of values may be of use both to us as researcher and to those parties with whom you
have contact in your research. These value judgments may lead to the drawing of conclusions
which may be different from those drawn by researchers with other values.
3.3.2 Research philosophy implemented:
As seen earlier researcher can adopt any philosophy related to their subject of research. In this
particular research, the researcher will adopt Positivism as nature of this study highly depends
on the strategic data collection and analysis. The researcher will be using existing compound
option theory developed by Merton (1974) and Geske (1977) to develop the research and also
will be extended further to prove integrated relationship between liquidity risk and credit risk.
This research will be implemented by using extended theory on collected sample which is
Citigroup’s financial statements ( 2002-2011) and also will be supported by using the Finch
Rating’s rating for Citigroup for same duration (2002-2011). The researcher will act
independently as research will depend on highly structured methodology and statistical analysis.
Collected data used in this research are also based on facts and statistical analysis, therefore
Positivism will be more appropriate philosophy for the researcher to carry out this research.

3.4 Research approaches:
There are two different types of approaches researcher can choose from for their research. One
is deductive and second is inductive approach. Deductive approach involves development of
theory through rigorous test or where researcher use general models on existing theory to enable
them reach to sensible and structured conclusion. This approach is highly organized and follows
the structured design. An Inductive approach normally starts with specific situation, finds its
contents, builds the theory and formulates the general models. Mostly in this approach author is
the part of the study. Compare to deductive approach it is very flexible in nature which helps the
researcher adjust his/her structure as he/she proceeds. Comparatively small samples are usually
suitable for this approach due to emphasis on the context in which phenomena are taking place.
3.4.1 Research approach chosen:
This research involves rigorous test of developed theory, Deductive approach will be ideal to
adopt and prove research proposed question. As defined by Robson (2002) there are five stages
in deductive approach to progress the research. First is deducting approach as the researcher will
use the existing Merton (1974) and Geske (1977) compound option theory, which will help
evaluating the relationship between liquidity risk and credit risk. Second will be explanation of
different variables to support extended model and formula of compound option theory proving
the integrated relationship between liquidity risk and credit risk, Third will be analyzing the
result of new formula against Citigroup’s financial data and at the same time rating of Citigroup
during the same time horizon to support the research, Fourth will be the critical analysis of the
outcome by comparing it with liquidity ratio suggested by Basel 3 for liquidity risk. The
researcher will confirm that whether the new proposed formula proves the relationship and
whether it is possible or not to use this theory to calculate liquidity and credit risk exposure of
particular company, Fifth and very important stage will be providing supported proofs
indicating the same results as the new theory to enhance the findings.
3.5 Research strategies:
There are numerous types of strategies that researcher can employ to conduct their research. It
also depends on which approach the researcher chooses for the research. Research strategy will
enable the researcher to answer their research question and meet their objectives. Among all of
them there are some strategies has been used most commonly are experiment, survey, case

study, action research, grounded theory, ethnography and archival research (Saunders et al,
2007).
The experiment strategy which relates more to the natural scientists however it is also used by
social scientists in their studies particularly in psychology. The main object of experiment is to
find whether the change in one independent variable led to a change in another dependent
variable therefor they mostly used in exploratory and explanatory to answer ‘how’ and ‘why’.
The survey strategy is mostly attached with deductive approach. It is most frequently used
strategy in business and management. They mostly used to answer who, what, where, how much
and how many questions and therefor tends to be used in exploratory and descriptive research.
They allow the collection of large amount of data in sampled population in highly economic
way. Highly structured interviews and highly organized questioner has been used for collection
of data. However it can cause delay in your research as researcher has to relay on others for
information. There is also a limit to number of questions researcher can add to their questioner.
There is another famous case study strategy has been define by Robonson (2002) ‘as a strategy
for doing research which involves an empirical investigation of particular contemporary
phenomenon within its real life context using multiple sources of evidence’. For example:
studying the performance of particular company in compare to the same industry, or in compare
to other company from same business nature. They could be defined by two discrete
dimensions, 1) Single case vs. multiple case 2) holistic case vs. embedded case (Yin, 2003).
The action research strategy has been interpreted many different ways by management
researcher (Saunders et al, 2009) and there are four main themes they have focused on, one
emphasizes on research in action rather than research about action (Coghlan and Brannick,
2005). The second emphasizes on involvement of practitioners in the research. The third theme
is the iterative nature of the process of diagnosing, planning, taking action and evaluating
(Saunders et al, 2009). The final theme implies that action research should have implications
beyond the immediate project (Saunders et al, 2009).
Ground theory can be defined as combination of inductive and deductive approach. According
to Goulding (2002), particularly helpful for research to predict and explain behavior, the
emphasis being upon developing and building theory. In ground theory data collection starts
without the frame work of theory and theory is developed from the data gathered from
observation.
Ethnography strategy is built in the inductive approach. This research process is flexible and
responsible in terms of change as researcher will constant develop new form of thoughts about
what is being observed during the timeline. It is by nature very time consuming as it takes place
over an extended time period as researcher has to devote their selves in the particular world
which is being researched.

In Archival research strategy data has been collected from administrative records and documents
as the principle source of data. It is useful to the types of question which is focus upon the past
and changes over time to be answered. They could be exploratory, descriptive or explanatory.
3.5.1 Research strategies employed:
As the researcher has adopted positivism philosophy and deductive approach to this research,
experiment strategy will be perfect combination to conduct this research. The researcher is
experimenting that whether a change in one independent variable (liquidity of particular bank)
led to a change in another dependent variable (credit risk of the same bank) in another words
whether there is link between both of them in terms of financial situation of the particular bank.
At the same time Archival strategy will be considered in to the research as use of administrative
records of Citigroup’s financial statements of last ten years will be used to employ the theory
3.6 Time horizons:
Time horizon is very important part of research. It depends on research question that it should
be short like “snapshot” which is called cross- sectional or it should be descriptive like “diary”
which is called longitudinal. Longitudinal studies normally used to shows the study of events
occurring over the year while cross – sectional studies are finish within the given period of time.
As this research is undertaken for academic qualification a cross sectional time horizon has been
chosen due to limited time limit given for research submission.
3.7 Research choice of techniques and procedures:
This section discuss in detail about data sourcing, benchmarking, choice of analytical
techniques and procedures used for interpretation and presentation of the data.
3.7.1 Data sources:
Primary data: Data which is collected for first time by the researcher relating to the subject
studied. It may include interviews, observation and use of questionnaires.
Secondary data: Data which is already collected for some other purposes. It includes raw data
and published material.

3.7.1 (A) Implementation of sources:
As researcher is conducting experimental research, probability sampling or in other words
representative sampling will be taken to obtain research objective. As this research requires the
sample of banks which was in the default situation due to their liquidity problem or was bailed
out stating the same liquidity problem in their firm during subprime crisis so that researcher can
use their financial data to prove the extended theory that liquidity risk exposure in particular
firm can result in to credit risk in another words (distance to default) which can be calculated
using compound option formula suggested by this theory. As the time available for research is
constrained the researcher is choosing only one bank (Citigroup) which was bailed out in 2008
due to their liquidity crisis.
The researcher heavily relies upon online and published secondary data. Citigroup’s annual
reports for last ten years (2002-2011) will be used in the research and downloaded from NYSE
website. Basel 3 regulatory guide lines for banks will be downloaded from the Basel
committee’s PDF documents available online (particularly related to Liquidity regulations).
Study Texts, Newspapers, Journals, Articles will be used to enhance the knowledge of subject
for the researcher to be able to define the constructive reasoning in the research.
London School of Economics library and London School of Business and finance’s library and
risk management lecture notes used by the researcher through the research.
3.7.2 Bench marks:
Benchmark is a predetermined standard by which something can be measured or judged and it
used as reference point.
3.7.2(A) Benchmark used for this research:
Analyses of liquidity risk or credit risk of any particular firm or country requires the benchmark
against which their performance can be measured and compared. The major benchmark in this
assessment will be Basel 3. Basel committee has concentrated on liquidity risk measurement
and credit risk of the banking industry after subprime crisis. There essential components of the
recommended guidelines will be the main bench mark to compare Citigroup’s performance
during subprime crisis. Main part of bench mark will be liquidity ratio defined in Basel 3 for
liquidity measurement of banking industry. The liquidity coverage ratio has been used to assess
exposure to contingent liquidity events. It suggests that the value of the ratio should be over or
equal to 100% at all times. Ratio should be calculated on the next 30 calendar days in to future.
The other benchmark will be used is Finch Rating’s rating for last ten years (2002-2011) for
Citigroup to compare the result of the research and analyze against the rating of the Citigroup
during subprime crisis.

3.8 Research choice, Data analysis and Presentation:
There are two different approach researcher can choose from, one is qualitative and second is
quantitative for interpretation, analysis and presentation of collected data.
Qualitative data: Any data which is not in numerical terms or data that cannot be quantified in
relation to the research question, objective, and aim of the research and also not processed or
analyzed for research is Qualitative data. Qualitative data only involves opinions, views and
comments about the subject of the research. Qualitative research can use both inductive and
deductive approaches. In qualitative research inductive approach can be used while collecting
data and analyzed it to make choice of particular subject to concentrate and deductive approach
can be used when researcher use any existing theory to formulate the research question and its
aim and objectives.
Quantitative data: It involves any numerical, statistical or quantifiable data which can be
measure in any form and has least meaning without being analyzed or processed to most of
people. Researcher needs to analyze quantitative data to make more meaningful and useful to
use in their research. There are many analytical techniques like tables, charts and graphs for
quantitative data. There are also many different types of software has been introduced in market
which can be used to interrelate the data and transfer in to presentational form and can be
interpreted in static form like SNAPTM
, SASTM
, SPSS, mini tab and Word excel.
3.8.1 Research choice implemented:
Researchers have different research choices for their research which depends on their question
of research and also objectives of their research. Researchers can adopt mono method or can
choose from multi method or mixed methods. It also depends whether their data is quantitative
or qualitative. They can also use mixture of both of them if it is suitable to their type of
research. Here in this research the researcher will be using Mono method which involves only
collection of secondary quantitative data. As Citigroup’s financial statements will be used in
compound option formula, Liquidity coverage ratio from Basel 3 regulatory guide lines will be
used to compare the outcome of the compound options, and also ratings from Finch Rating will
be imply on the findings to analyze whether these elements are suggesting similar or different
movements on the same timeline. To evaluate this study graphical representation will be used to
highlight their moves.
Researcher will be using Excel and VBA software to calculate compound option and make these
data presentable in comparative manor.
Descriptive statistics in quantitative research which will help the researcher to evaluate the
relationship between two variables will be implemented as mentioned in research strategy.

3.9 Ethics and Corporate Governance:
Ethics is main determinant for researchers to take in to account during their research process. It
provides the discipline boundary which researcher should not be cross while conducting their
research. The researcher has adopted basic principle to carry out this research (Bryman et al
2003).
1) There is no lack of informed consent.
2) Privacy of any kind hasn’t been bridged.
3) There is no deception involved.
4) The researcher’s writing is not proposing any unprofessional opinion about respected authors.
3.10 Research methodology implemented:
The researcher will present the layout defining different stages of the whole research. In the first
stage the researcher will discuss types of theories used in this research. In the second stage
methods implemented for the reclassification of the variables of the compound option will be
presented with explanation in detail about the data selected for them. In the third stage, the
reasoning will be provided to support the research. In final stage the researcher will describe the
determined limitations that are imposed during the research process.
3.10.1 Theories used for the research:
The researcher will start with basic theories of options and types of options and will carry on to
further explain the theories which have been adopted to carry this research. This will include the
explanation of basic terminology and definitions.
Option is type of financial derivative which represents a contract of right to buy or sell but not
the obligation of underlying assets or a contract of security in future at defined date and at
defined time. Where, financial derivative is a security whose price derived from one or more
underlying assets (Hull 2007). The option contract which represents the right to buy an asset or
security but not the obligation is called a Call option. On the other hand, the option contract
which represents the right to sell and not the obligation is called a Put option. Option consist
one strike price which is also known as the exercise price. If option will be exercised, it will be
exercised with the exercise price as it was agreed on the contract (Hull, 2007).
As explained earlier option contract can be used for underlying assets or can also be used for
dealing on another option. It means that it is also possible to buy or sell an option on an option.
This type of option on an option is known as Compound option. The exercise price of the
compound option will be the price of the underlying option. Therefore, there will be two strike
prices and two expiration dates. There are four types of compound options Call on a call, Put on

call, Call on put, Put on a call. For Example, in a compound option when borrower will buy
European Call on call, the borrower will purchase a compound option at time T0, which will
give the borrower the right to buy a second option. That compound option can be exercised by
the same borrower at time T1 by paying the strike price K1. Therefore, the borrower with that
compound option will exercise it with the condition that the value of the underlying call option
will be greater than strike price K1. Now that the borrower owns the underlying call option with
another strike price K2, the borrower has the right to exercise that second option at T2. Again at
T2 borrower will only exercise the call option if the value of the underlying assets (s) of that
second option is greater than strike price K2 and then he/she will receive the underlying assets in
return and at the maturity date T2. Hull (2007) has defined Call on call in formulated manor as
mentioned below.
Call on call: max{C(S, T1) − K1, 0}
In European Put on call option the borrower will buy a compound option at time T0, which will
give the borrower the right to sell a second option which is call option. That compound option
can be exercised by borrower if he/ she sell that option to the buyer by receiving the strike price
K1 at T1. The buyer in return will receive the underlying option which is call option. Now, the
underlying call option will have another strike price K2 and another expiration date T2. Hull
(2007) has defined put on call in formulated manor as mentioned below.
Put on call: max{X1 − C(S, T1), 0}
3.10.1(A) Merton’s call option
Merton’s call option (1974) is very popular approach to assess credit risk of the company.
Merton suggests that equity of the company can be treated as call option on the company’s
assets with maturity T and the strike price of the option will be the face value of the total debt.
As this call has maturity time it only can be exercise on its maturity, which is called European
call option. At maturity date if company’s assets value is greater than its face value of debt the
company will default and company will go to bondholders and shareholders will get nothing.
This model assumes that company has certain amount of zero-coupon bond that will become
due at a future time T.

3.10.1(B) Geske’s compound option (1977)
Geske’s compound option is based on Merton’s call option. This method is useful to get the
value of many corporate liabilities. Using the Merton option in his compound option his theory
suggests that bondholders own the firm’ s assets and they have given option to shareholders to
buy the assets back when the bonds will become mature. That means now call on the firm stock
is compound option. He assumes that bonds are pure discount bonds and gives the bond holder
the right of face value at maturity. Firm also does not declare any dividend prior to maturity of
bonds.
3.10.1(C) Maltritz model (2009)
As we discussed in literature review Maltritz has adopted compound option to interrelate
banking crisis and country defaults. The researcher has adopted the compound option to propose
integrated relationship between liquidity risk and credit risk which is similar option to Maltritz.
Maltritz proposed option that is also based on Geske’s (1977) option offering multiple payments
at different dates. The researcher also will need option with multiple payments which has to be
made at different dates depending on liquidity required to bail out Citi group at different dates
and credit risk exposure (default) will occur in any future date.
3.10.1(D) Hui-Lo valuation model (2000)
Hui-Lo (2000) presents the model to address the default situation. In his words “Default occurs
when some signaling process hits a pre- defined default barrier”. Foreign exchange rates
represent the signaling variables. His theory adopts structural model (Suggested by Merton
(1974), Black and Scholes (1973)) and reduced form model to price defaultable bonds. His
model assumes the signaling process that defines the default occurrence for the firm rather than
asset value of the firm. The researcher’s work will also be following the same structural model
to define her default situation like Hui-Lo and her framework will reflect the spirit of his theory
in her research.
3.10.2 Proposed compound option by researcher:
The researcher is proposing her compound option as Put on call where shareholders have right
to sell underlying option (Merton call option) to Central bank. Shareholders will exercise their
right to sell when Citigroup will be in liquidity risk meaning their short term liquid assets will
not be able to meet the short term obligations. Citigroup will receive strike price K1 at time T1.

Here, K1 is considered as the liquidity bailout price (short term liabilities) for Citigroup. Now,
central bank will own an underlying option which will be call option (Merton call option). If the
value of the underlying call (the Merton Call) is greater than that strike price K1 Central bank
will exercise their call option which is call option for underlying assets and the underlying asset
is assumed to be the wealth (Total net assets) of the company. Now, at T2, the Central bank will
be able to exercise the second option (Merton Option) by paying the strike price K2, meaning
that Citigroup will be in a default in Merton terms (Assets Value < Liabilities Value). We
consider that K2 represents the total liabilities of Citigroup.
Formula used for compound option:
The researcher has used two different types of formula to calculate her compound option with
her proposed variables. The researcher has used Geske (1977) proposed formula in Excel with
VBA coding to get the results. The researcher has also adopted binomial compound option
formula to confirm her results arrived from first formula. Using two formulas for compound
option will help the researcher support her proposed compound option theory.
Assumptions:
The equity in Geske’s terms is, at the beginning, changes into my asset value. The researcher
assumes that there is one economy and one bank. Time duration between T0 and T1 has been set
at minimum 6 months duration for Cititgroup to be able to try every possible way to raise
money before central bank exercise their compound call. Researcher assumes there is no
dividend paid same as Merton call option. Volatility of value of assets has been count using
Merton’s Asset value formula.
3.10.3 Comparison with Basel 3 ratio:
Basel committee on banking supervision has reformed the structure after 2007 crisis. Their main
objective was to strengthen capital and liquidity regulation in banking sector. They were aiming
to make banking sector more resilient towards volatility in liquidity requirements after
experiencing the whole banking system shaken. There are two main ratios covering liquidity
risk defined by Basel 3. The first one is Liquidity Coverage ratio and the second one is Net
Stable Funding ratio. The researcher will be calculating the Liquidity coverage ratio to
determine the liquidity problems occur during the last 10 year in Cititgroup. The researcher will
assume the variables of Liquidity Coverage ratio from annual reports of Citigroup due to
unavailability of data required to calculate the ratio as defined guideline of the Basel 3.
Stock of High-quality Liquid assets
Total net cash outflows

In order to count Liquidity Coverage ratio the researcher has considered Basel 3 guide lines to
define High Quality Liquid Assets. Which consist of Cash due from banks, Federal funds sold
and securities borrowed or purchased under agreement to resell, U.S. government – sponsored
agency guaranteed (Available for sale assets), U.S. Treasury and federal agency Securities
(Available for sale assets), state and municipal (Available for sale assets), Foreign government
(Available for sale assets) as Level -1 assets, as they all are risk free assets by nature. The
researcher has considered deposits with bank and Brokerage receivables as Level -2 assets as
they carry lower grade risk. As per Basel 3 guideline, the calculation of Net cash outflow
consists of Retail deposits, unsecured wholesale funding, additional requirements and various
cash inflows. Basel 3 has also provided detailed guideline suggesting appropriate mixture of
various cash flows with defined propositions which depends on their characteristics.
Assumptions for LCR (Liquidity Coverage Ratio):
The researcher had limited access to financial data needed to calculate this ratios, therefore all
assumptions as mentioned below has been taken to follow the guidelines of Basel 3 to enhanced
results. Level -1 and Level -2 assets are independent to each other, which mean that any change
in one of their value should not affect the value of the other assets. ‘Brokerage receivables’
carries the risk of not being paid but as Citigroup maintains margin collateral in compliance
with regulatory requirements (Citigroup annual report 2011), these margin levels are monitored
on daily bases. Therefor the researcher assumes that brokerage receivables does not carry more
than 20% risk and can be eligible for Level -2 assets. Level -1 and Level -2 and net operational
cash flow have been taken on yearly basis and proportioned to enact value on monthly basis.
Retail deposits consists unstable and stable deposits which is not possible to be categorized
from the annual reports and since the researcher did not have access of Citigroup’s management
accounts, the researcher has adopted the average of both the stable and unstable deposits which
is 7.5% (BASEL 3 requirement : stable deposits 5%, unstable deposits 10%). Short term
borrowing has been taken from the annual financial statements and will be assumed to be paid
in equal installments through the year. Brokerage payables have also been taken from annual
financial statements and will be assumed to be paid in equal amounts. Trading account liabilities
includes corporate and other funding hence average 50% of it is to be assumed as outflows.
Long term liabilities include secured assets and 50% of secured assets is assumed as outflow
and proportioned for monthly basis. Other liabilities may include additional requirements (Basel
3 guidelines) and 50% of it is assumed as fully payable in month. Cash inflows has been taken

as 15% of other Level 2 assets, and 75% brokerage receivable as it can be containing amount
receivable from financial institutions from other transactions which has been used 100%.
After evaluating compound option values from last 10 years, the researcher will calculate LCR
(Liquidity Coverage Ratio) as mentioned above for the Citigroup for the same time horizon as
compound option. The researcher will adopt the formula suggested by the Basel 3 regulation for
calculation. Then the outcome of the ratio which suggests the liquidity position of the company
on monthly basis and funding ability of the company will be compared with the result of the
compound option. The researcher will then analyze, if the company’s liquidity suggested by the
ratios follows the same direction the way it was presented from result of the compound option.
If the outcome shows the movements in the same direction that will back up the researcher
proposal and will support her reasoning with evidence.
3.10.4 Bench mark implementation:
Outcome of the valuation of the compound option which was applied to the last 10 years data of
Citigroup will be presented in a chart and credit rating for the same time horizon of Citigroup
will be highlighted to support the analysis by showing the “correlation” between them.
According to hull (2007) “This ideally should be showing that when value of the option
increase, i.e. amount of necessary bailout is increasing, the rating will decrease – On the other
hand, when value of the option will decrease (i.e. amount of necessary bailout is decreasing),
then the rating will increase. That will support the researcher’s proposal.

Chapter: 4 – Research Analyses
This chapter will focus on types of data that have been collected, how they have been collected,
what that data means in this analysis, calculations of collected data, interpretation of the
calculations and how does it support to answer the researcher’s question. Firstly, the researcher
will discuss about the proposed compound option and its calculations. Secondly the researcher
will move on to Liquidity ratios, its variables and their calculations, Thirdly the researcher will
collect the credit ratings of the Citigroup’s financial performance for the defined time line which
is 2002 – 2011, And lastly the researcher will bring these data together, present the
interpretation of this data in the light of the research question and the outcome of these
calculations in return of the researcher’s proposed question.
4.1 Proposed Compound option
As explained in previous chapter the compound option is an option on an option. Therefore,
there are two strike prices, two expiry dates of the options and the underlying assets. The
researcher also needs to find out underlying assets on which the compound option is based on.
There are few other factors that are necessary to define before going to compound option
calculations such as risk free rate, dividend yield and volatility in the value of the assets during
the defined timeline. Compound option can be calculated using Black-Scholes, Binomial trees,
Monte Carlo Simulations and many more.
Black – Scholes is a closed form formula and has been implemented and elaborated by Geske
(1977) and Rubistein (1991) to price European compound options. Black – Scholes formula
assumes that it is risk neutral world and expected option value can be discounted at the expiry
date with risk free rate. It also assumes there is constant volatility which was challenged by
Geske (1977). Geske suggested that volatility of value of the assets does not stay constant in
real life and he extended Black –Scholes formula by adopting volatility calculations from
Merton’s volatility formula.
The alternative way of calculating compound option is Monte Carlo Simulations which is based
on algorithm and use repeated random sampling to calculate results. This model implements n
simulations of uniform variables which transforms in to normal variables. It uses these variables
to simulate S with geometric bownian motion, R with short rate interest models and V with the
Heston model. These three imposes the payoff of the compound option.
Binomial option pricing model evaluates the option’s underlying variables in discrete time. As it
follows the underlying variables over the period of time and not at any single time defined like
in other models. It also known as the binomial tree model as it consist number of time steps

between the valuation and its expiration dates. Each of these trees will show possible price of
the underlying assets at that particular time.
The researcher has calculated the compound option using Geske(1977) extended formula of
compound option which is based on Black–Scholes, as researcher also believe that volatility of
value of assets does not stays constant. The researcher has adopted Excel based compound
option formula to calculate the compound option prices. This Excel based formula is supported
by Visual Basic Programming. Coding for this programming has been attached in to appendix
(C). The researcher is also using Binomial formula from Excel to calculate compound option
pricing. Using two types of models to calculate compound option pricing will help researcher to
make her reasoning strong as outcome of both option pricing will show same movements during
the defined time lines.
All variables of compound option have been counted for total of 10 years starting from 2002 to
2011 as it consist of the period before Cititgroup started facing trouble and after their survival
through the crisis. Total assets of the company at the end of the every fiscal year has been taken
as underlying assets of the compound option as they represent the wealth of the company. The
first expiry date of the compound option will be at the end of every 6 months, as if Citigroup
will be measuring their liquidity exposure every month, they will need some time to solve the
liquidity problems after they recognize the issue. The researcher will also assume that Central
bank’s supervisors will also allow the company to have some time equivalent to 6 months to
overcome the issue in practice. The second expiry date of the compound option also known as
the expiry date of underlying assets will be at the end of the fiscal year. This means that first
date of every New Year, because the underlying assets in our compound option is the wealth of
the company (total net assets) and it can only be recognized after the declarations of accounts at
the end of the fiscal year. So the first expiration date at T1 will be at every 6 months and the
second expiry date at T2 will be 6 months and one day from T1 or in other words, it will be at
every fiscal year end. The first strike price of the compound option ‘K1’ will represent the price
of the compound option at the first expiry date. This have been counted by including the total
run on deposits compared with the last year (current year total deposits – Last year deposits,
only if it is negative), means if total deposits has been reduced compared to last year, then
liquidity has gone down as deposits represents the liquidity of the company means Increase or
decrease in amount of deposits directly related to the availability of the liquidity of the
company. Amount of total interest payments on these deposits are also included in calculating
‘K1’ strike price as the bank also pays the interest on these deposits on continues basis and will
need the funds to fulfill this payments. Now, ‘K1’ will be total of run on deposits as stated earlier
and total interest payments. These data has been taken from Citigroup’s financial statements and
have been attached in appendix (B). The second strike price of the compound option K2 which
will represent the price of the underlying assets at the end of the second expiry date, which will

be the total net liabilities of the company. As underlying assets (Call option of the compound
option ) is based on Merton’s theory which represents if the Total assets compare to total
liabilities of the firm is lower than firm is in default. By taking total net liabilities as K2 for the
underlying assets (wealth of the company) the researcher will also find out the default situation
of the firm. The total liabilities will be taken from Citigroup’s financial statements. Volatility of
the under lying assets value have been derived using Merton’s Value of assets formula in Excel.
Valuations showing the volatility during the time line of analyses have been attached to
Appendix (D). To be able to count the volatility the researcher first of all have gathered data
consisting market value of equity of Citigroup’s on daily basis, book value of liabilities on daily
basis, risk free rate on daily basis. The researcher has used Yahoo finance data for market value
of liquidity. The researcher has taken book value of liabilities from the Citigroup’s financial
statements for stated ten years. Risk free rate as one year constant maturity rate has been
downloaded from Federal Reserve of St Louis (Economic Research). The researcher assumes
that there is no dividend as her compound option model is based on Merton and Geske which
also assumes there is no dividend has been paid.
Table 1 – Compound option variables
(value in millions of dollars )
Year
Run on
deposits +
interest
payments K1
Net Total
Liabilities
K2
Under
lying
Assets S
Risk
free
rate
2011 24,234 1,694,305 1,873,878 2.78
2010 25,096 1,748,113 1,913,902 3.22
2009 27,092 1,701,673 1,856,646 3.26
2008 104,795 1,794,448 1,938,470 3.66
2007 75,958 2,074,033 2,187,480 4.01
2006 55,683 1,764,535 1,884,318 4.27
2005 36,676 1,381,500 1,494,037 4.29
2004 22,004 1,374,810 1,484,101 4.61
2003 17,184 1,166,018 1,264,032 4.63
2002 21,248 1,010,872 1,097,590 4.80
[Source: Appendix (A)]
After, calculating all variables as shown in the table 1 above for compound option values they
have been applied to the Excel compound option formula to get the prices for option values. As
mentioned above K1 consist of run on deposits compare to last year and interest paid for the
deposits, by looking at the figures in table 1 their liquidity position was stable from 2002 to

2005, and started increasing dramatically from2006 to 2008. This dramatic difference shows
that Cititgroup was running short of deposits, which is the main source of banks to satisfy their
liquidity needs. This figure shows that this short of liquidity was not just over the night situation
but was gradually building up (in Millions) since 2003. At the same time if we look at the K2
which represents the net total liabilities of Cititgroup was increasing slowly compare to its short
term liabilities from 2002 to 2007. In 2008 it went down as Cititgroup was bailed out by the
government in November 2008. Underlying assets which are the total of net assets are
increasing gradually from 2002 to2007. This supports the statements the researcher made earlier
that Cititgroup was in short of liquidity which lead the bank to bail out position. In next step the
researcher will represent the result of the compound option price calculations using variables
from Table 1.
Table 2 – Values of compound option
Year
Geske
Put on call
Binomial
Put on call
2011 393487.57 394261.23
2010 409902.53 411523.62
2009 402352.39 404285.22
2008 472402.46 476903.80
2007 535405.51 540556.16
2006 440931.26 444867.14
2005 334969.99 337462.58
2004 324725.08 326822.03
2003 272814.35 274367.30
2002 238992.75 240506.52
[Source: calculated using VBA coded excel sheets attached in appendix C]
Table 2 represents the Compound option which is Put on call as the researcher explains her
compound option as Shareholders have right to sell (Put option) the right to buy( underlying
call option) to central bank, which Citigroup will only exercise if Citigroup will be in liquidity
trouble . By exercising the put option to central bank, Cititgroup will get the money to save their
frim from liquidity and central bank will then own the underlying call option. Here, the
underlying option is the normal call option (Merton option) where, equity is the underlying
option on the value of the firm. In other words, if central bank will have right to exercise their
call option and will buy the equity shares of the Citigroup.
By looking at the prices of compound options, it has been slowly increasing from 2002 to 2007
same as liquidity shortage (K1). It shows that as liquidity exposure increases price of the option
increases relatively so there is a correlation between liquidity and compound option price. The

researcher has calculated compound option prices using two formulas as stated before, one is
using Geske’s formula and the other one is binomial formula. The researcher’s compound
option is based on Geske and Merton theories. The researcher has calculated binomial
compound option prices to support her first result of compound option which can be seen in the
table 2. Both results of compound options in table shows they are very closer to each other’s
value and increases simultaneously from 2002 to 2007. Compound option prices have been also
jumped in millions from 2005 to 2006 and from 2006 to 2007. These changes can be interlinked
to direct effect of the K1.
Graph 1- Price for put on call option using Geske and Binomial method.
This graph represents the time line on the X axis, and price of the compound option on the Y
axis. The value of the compound option has been derived on yearly basis. Drawing the graph
makes it easy for researcher to interpret the compound option scenario. It also shows that using
the compound option it is possible for firm to measure their liquidity position and credit risk
exposure. Next the researcher will add more support to her reasoning by calculating liquidity
coverage ratios for the same timeline.
0.00
100000.00
200000.00
300000.00
400000.00
500000.00
600000.00
2011 2010 2009 2008 2007 2006 2005 2004 2003 2002
Geske Put on call Binomial Put on call

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