Balance-sheet dynamics impact on FVA, MVA, KVAAndrea Gigli
Β
In this talk I show how balance-sheet dynamics and changes in the Asset/Liability portfolio have and impact on the calculation of FVA, MVA and KVA through a simple multi-period structural model.
Impact of Valuation Adjustments (CVA, DVA, FVA, KVA) on Bank's Processes - An...Andrea Gigli
Β
The talk hold in London on September 10th at the 5th Annual XVA Forum on Funding, Capital and Valuation. It covered some implications of Valuation Adjustments like CVA, DVA, FVA and KVA (XVAs) in the Pricing of Derivatives, Data Model Definition, Risk Management, Accounting, Trade Workflow processing.
Dr. Tony Webb, Director of Analytics, FINCAD lead a discussion on CVA best practices and current techniques at Random Walkers Roundtable on CVA organized by Maroon Analytics and hosted by 7city Learning. Random Walkers is a regular, open discussion on current topics in quantitative finance. With topics proposed by participants, each session is led by an expert in the field and is formatted to encourage active participation from all attendees.
FINCAD's F3 is a fast & flexible CVA pricing solution. Watch a demo at http://bit.ly/Rdv7lf
RiskAsean 2017: the relevance of CVA & XVAs in Asia Alexandre Bon
Β
1. OTC derivatives valuation after the global financial crisis
2. XVA from the economic, accounting & regulatory viewpoints
3. XVA management & Asia specific challenges
4. The new Margining rules & FRTB CVA charge: potential game changers?
RiskMinds - Did Basel & IOSCO put the final nail in the coffin of CSA-discoun...Alexandre Bon
Β
FVA in presence of stochastic funding spreads, Inititial Margins and imperfect collateralisation conditions.
Since the birth of CSA discounting during the GFC, major regulatory changes have been reshaping collateral practices in a way that challenges the fundamental assumptions of the method.
Agenda:
- FVA via CSA discounting or Exposure simulation
- Funding spreads and exposure co-dependence
- Collateralisation regimes in the New Normal and Initial Margins
- FVA/MVA for VaR-based IMs and the SBA-M
- FVA for economic value & incremental pricing
Balance-sheet dynamics impact on FVA, MVA, KVAAndrea Gigli
Β
In this talk I show how balance-sheet dynamics and changes in the Asset/Liability portfolio have and impact on the calculation of FVA, MVA and KVA through a simple multi-period structural model.
Impact of Valuation Adjustments (CVA, DVA, FVA, KVA) on Bank's Processes - An...Andrea Gigli
Β
The talk hold in London on September 10th at the 5th Annual XVA Forum on Funding, Capital and Valuation. It covered some implications of Valuation Adjustments like CVA, DVA, FVA and KVA (XVAs) in the Pricing of Derivatives, Data Model Definition, Risk Management, Accounting, Trade Workflow processing.
Dr. Tony Webb, Director of Analytics, FINCAD lead a discussion on CVA best practices and current techniques at Random Walkers Roundtable on CVA organized by Maroon Analytics and hosted by 7city Learning. Random Walkers is a regular, open discussion on current topics in quantitative finance. With topics proposed by participants, each session is led by an expert in the field and is formatted to encourage active participation from all attendees.
FINCAD's F3 is a fast & flexible CVA pricing solution. Watch a demo at http://bit.ly/Rdv7lf
RiskAsean 2017: the relevance of CVA & XVAs in Asia Alexandre Bon
Β
1. OTC derivatives valuation after the global financial crisis
2. XVA from the economic, accounting & regulatory viewpoints
3. XVA management & Asia specific challenges
4. The new Margining rules & FRTB CVA charge: potential game changers?
RiskMinds - Did Basel & IOSCO put the final nail in the coffin of CSA-discoun...Alexandre Bon
Β
FVA in presence of stochastic funding spreads, Inititial Margins and imperfect collateralisation conditions.
Since the birth of CSA discounting during the GFC, major regulatory changes have been reshaping collateral practices in a way that challenges the fundamental assumptions of the method.
Agenda:
- FVA via CSA discounting or Exposure simulation
- Funding spreads and exposure co-dependence
- Collateralisation regimes in the New Normal and Initial Margins
- FVA/MVA for VaR-based IMs and the SBA-M
- FVA for economic value & incremental pricing
Global Derivatives 2014 - Did Basel put the final nail in the coffin of CSA D...Alexandre Bon
Β
FVA in presence of stochastic funding spreads, Inititial Margins and imperfect collateralisation conditions.
Since the birth of CSA discounting during the GFC, major regulatory changes have been reshaping collateral practices in a way that challenges the fundamental assumptions of the method.
Agenda:
- FVA for economic value & incremental pricing
- FVA via CSA discounting or Exposure simulation
- Funding spreads and exposure co-dependence
- Collateralisation regimes in the New Normal and Initial Margins
Long horizon simulations for counterparty risk Alexandre Bon
Β
The Challenges of Long Horizon Simulations in the context of Counterparty Risk modeling : CVA, PFE and Regulatory reporting.
This joint presentation reviews the key decisions that need making regarding the choice of risk factor evolution models and calibration methods. In particular, we will analyse the performance of classical historical calibration methods (such as Maximum Likelihood and the Efficient Method of Moments) in estimating the volatility and drift terms of the Hull & White class of Interest Rate models ; both in terms of convergence and stability.
As most methods perform satisfactorily for volatility but disappoint on the mean reversion estimation, we propose a new modified Variance Estimation method that significantly outperform the classical approaches.
Lastly, after reviewing historical economic evidence of mean-reversion dynmics in high interest rate regime, we propose modifying classical models by making mean reversion non-linear and accelerating for high rates - that can be referred as "+R" models.
This model address unrealistically large and persistent interest rates values often observed at high quantile in PFE and CVA simulations.
OTC Collateralisation : implementations issues in the context of CVA & FVA
- The ideal CSA hypothesis : Imperfect collateralisation for credit mitigation and/or funding
- FVA vs. CSA-discounting
- Implications in terms of curves calibrations and management
- FVA for Cleared positions
- FVA or CSA-discounting : which funding management model?
These Lecture series are relating the use R language software, its interface and functions required to evaluate financial risk models. Furthermore, R software applications relating financial market data, measuring risk, modern portfolio theory, risk modeling relating returns generalized hyperbolic and lambda distributions, Value at Risk (VaR) modelling, extreme value methods and models, the class of ARCH models, GARCH risk models and portfolio optimization approaches.
The presentation highlights some shortcut formulas that can speed up PV computations if a project have a particular set of cash flow patterns and the opportunity cost of capital is constant
Global Derivatives 2014 - Did Basel put the final nail in the coffin of CSA D...Alexandre Bon
Β
FVA in presence of stochastic funding spreads, Inititial Margins and imperfect collateralisation conditions.
Since the birth of CSA discounting during the GFC, major regulatory changes have been reshaping collateral practices in a way that challenges the fundamental assumptions of the method.
Agenda:
- FVA for economic value & incremental pricing
- FVA via CSA discounting or Exposure simulation
- Funding spreads and exposure co-dependence
- Collateralisation regimes in the New Normal and Initial Margins
Long horizon simulations for counterparty risk Alexandre Bon
Β
The Challenges of Long Horizon Simulations in the context of Counterparty Risk modeling : CVA, PFE and Regulatory reporting.
This joint presentation reviews the key decisions that need making regarding the choice of risk factor evolution models and calibration methods. In particular, we will analyse the performance of classical historical calibration methods (such as Maximum Likelihood and the Efficient Method of Moments) in estimating the volatility and drift terms of the Hull & White class of Interest Rate models ; both in terms of convergence and stability.
As most methods perform satisfactorily for volatility but disappoint on the mean reversion estimation, we propose a new modified Variance Estimation method that significantly outperform the classical approaches.
Lastly, after reviewing historical economic evidence of mean-reversion dynmics in high interest rate regime, we propose modifying classical models by making mean reversion non-linear and accelerating for high rates - that can be referred as "+R" models.
This model address unrealistically large and persistent interest rates values often observed at high quantile in PFE and CVA simulations.
OTC Collateralisation : implementations issues in the context of CVA & FVA
- The ideal CSA hypothesis : Imperfect collateralisation for credit mitigation and/or funding
- FVA vs. CSA-discounting
- Implications in terms of curves calibrations and management
- FVA for Cleared positions
- FVA or CSA-discounting : which funding management model?
These Lecture series are relating the use R language software, its interface and functions required to evaluate financial risk models. Furthermore, R software applications relating financial market data, measuring risk, modern portfolio theory, risk modeling relating returns generalized hyperbolic and lambda distributions, Value at Risk (VaR) modelling, extreme value methods and models, the class of ARCH models, GARCH risk models and portfolio optimization approaches.
The presentation highlights some shortcut formulas that can speed up PV computations if a project have a particular set of cash flow patterns and the opportunity cost of capital is constant
Liquidity risk is one of the major risks inherent in the banking business. It occurs when the bank does not have sufficient liquid assets to meet its commitments at the time of their occurrence. The most critical challenges confronting financial institutions when managing liquidity risk is so-called non-maturity accounts. These accounts are characterized by the fact that they have no specific contractual maturity, and their risk management is complicated by the embedded options that depositors may exercise. As part of an asset-liability management and for the purpose of healthy and prudential management of a liquidity risk, each bank must properly assess the deposits of its customers. Liquidity risk is not the risk that there are massive withdrawals, but the risk they are unanticipated. In this paper, we apply two methods to model non-maturity deposits of a Moroccan commercial bank. We treat separately individual deposits and enterprise deposits aiming an accurate analysis. We then select between the models by means of a selection criteria. Furthermore, we back-test and forecast future deposits using the selected model. Finally, we model the decay rates of non-maturity deposits by elaborating a flowing function of these latter.
Credit risk refers to the risk that a borrower will default on any type of debt by failing to make payments which it is obligated to do. The risk is primarily that of the lender and includes lost principal and interest, disruption to cash flows, and increased collection costs. The loss may be complete or partial and can arise in a number of circumstances. For example:
β’ A consumer may fail to make a payment due on a mortgage loan, credit card, line of credit, or other loan
β’ A company is unable to repay amounts secured by a fixed or floating charge over the assets of the company
β’ A business or consumer does not pay a trade invoice when due
β’ A business does not pay an employee's earned wages when due
β’ A business or government bond issuer does not make a payment on a coupon or principal payment when due
β’ An insolvent insurance company does not pay a policy obligation
β’ An insolvent bank won't return funds to a depositor
β’ A government grants bankruptcy protection to an insolvent consumer or business.
To reduce the lender's credit risk, the lender may perform a credit check on the prospective borrower, may require the borrower to take out appropriate insurance, such as mortgage insurance or seek security or guarantees of third parties, besides other possible strategies. In general, the higher the risk, the higher will be the interest rate that the debtor will be asked to pay on the debt.
cash management
Strategies for cash management
Projection of cash flows and planning
Determining optimal level of cash holding in the company
(EOQ) to cash management
a) (Economic Order Quantity) to cash management
b) Stochastic model
c) Probability model
Miller and Orr model
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
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or
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Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
β help.mbaassignments@gmail.com β
or
Call us at : 08263069601
(Prefer mailing. Call in emergency )
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
β help.mbaassignments@gmail.com β
or
Call us at : 08263069601
(Prefer mailing. Call in emergency )
Dear students get fully solved assignments
Send your semester & Specialization name to our mail id :
β help.mbaassignments@gmail.com β
or
Call us at : 08263069601
(Prefer mailing. Call in emergency )
We are a Quantitative investment group committed to revolutionize the fund management industry in the country. We are using pure quant technique to create a zero loss fund (the fund will always be positive) i.e; all of your losses (if any) will be insured.
How organizations can become data-driven: three main rulesAndrea Gigli
Β
The presentation shows how organization can successfully become data driven and avoid wasting time and money. It explain how to prioritize business questtions, how to combine properly people, tech&data and processes, and how to structure a transforamtional journey for becoming a data driven.
Recommendation Systems in banking and Financial ServicesAndrea Gigli
Β
Robot advisory is a hot topic in Banking and Finance nowadays. The quality of any Robot relies on its ability to anticipate the choices of customers and engage them toward action. For this reason, recommendation systems are gaining ground in the banking sector as an alternative or supplementary approach to classical Portfolio Selection models. In this talk, I show how to build recommendation systems in Python using two different ideas, one inspired by graph theory, and the other by word embedding
Fast Feature Selection for Learning to Rank - ACM International Conference on...Andrea Gigli
Β
My talk on fast feature selection filter algorithms at the ACM International Conference on the Theory of Information Retrieval (ICTIR 2016) held in Newark, DE, US
Feature Selection for Document RankingAndrea Gigli
Β
Feature selection for Machine Learning applied to Document Ranking (aka L2R, LtR, LETOR). Contains empirical results on Yahoo! and Bing public available Web Search Engine data.
Comparing Machine Learning Algorithms in Text MiningAndrea Gigli
Β
In this project I compare different Machine Learning Algorithm on different Text Mining Tasks.
ML algorithms: Naive Bayes, Support Vector Machine, Decision Trees, Random Forest, Ordinal Regression as ML task
Tasks considered: Classifying Positive and Negative Reviews, Predicting Review Stars, Quantifying Sentiment Over Time, Detecting Fake Reviews
Presentazione Startup Saturday Europe @ ParmaCamp2013Andrea Gigli
Β
Startup Saturday Europe is a not-for-profit organization born to promote collaborative networking among Innovation Stakeholders in Europe. It started its activity in January 2013. In this presentation Andrea Gigli presents SSE mission and philosopy during Parmacamp 2013.
how can I sell pi coins after successfully completing KYCDOT TECH
Β
Pi coins is not launched yet in any exchange π± this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAYΒ you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
I and my friends has sold more than 6000 pi coins successfully with this method. I will be happy to share the contact of my personal pi merchant. The one i trade with, if you have your own merchant you can trade with them. For those who are new.
Message: @Pi_vendor_247 on telegram.
I wouldn't advise you selling all percentage of the pi coins. Leave at least a before so its a win win during open mainnet. Have a nice day pioneers β₯οΈ
#kyc #mainnet #picoins #pi #sellpi #piwallet
#pinetwork
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
Financial Assets: Debit vs Equity Securities.pptxWrito-Finance
Β
financial assets represent claim for future benefit or cash. Financial assets are formed by establishing contracts between participants. These financial assets are used for collection of huge amounts of money for business purposes.
Two major Types: Debt Securities and Equity Securities.
Debt Securities are Also known as fixed-income securities or instruments. The type of assets is formed by establishing contracts between investor and issuer of the asset.
β’ The first type of Debit securities is BONDS. Bonds are issued by corporations and government (both local and national government).
β’ The second important type of Debit security is NOTES. Apart from similarities associated with notes and bonds, notes have shorter term maturity.
β’ The 3rd important type of Debit security is TRESURY BILLS. These securities have short-term ranging from three months, six months, and one year. Issuer of such securities are governments.
β’ Above discussed debit securities are mostly issued by governments and corporations. CERTIFICATE OF DEPOSITS CDs are issued by Banks and Financial Institutions. Risk factor associated with CDs gets reduced when issued by reputable institutions or Banks.
Following are the risk attached with debt securities: Credit risk, interest rate risk and currency risk
There are no fixed maturity dates in such securities, and assetβs value is determined by companyβs performance. There are two major types of equity securities: common stock and preferred stock.
ο Common Stock: These are simple equity securities and bear no complexities which the preferred stock bears. Holders of such securities or instrument have the voting rights when it comes to select the companyβs board of director or the business decisions to be made.
ο Preferred Stock: Preferred stocks are sometime referred to as hybrid securities, because it contains elements of both debit security and equity security. Preferred stock confers ownership rights to security holder that is why it is equity instrument
<a href="https://www.writofinance.com/equity-securities-features-types-risk/" >Equity securities </a> as a whole is used for capital funding for companies. Companies have multiple expenses to cover. Potential growth of company is required in competitive market. So, these securities are used for capital generation, and then uses it for companyβs growth.
Concluding remarks
Both are employed in business. Businesses are often established through debit securities, then what is the need for equity securities. Companies have to cover multiple expenses and expansion of business. They can also use equity instruments for repayment of debits. So, there are multiple uses for securities. As an investor, you need tools for analysis. Investment decisions are made by carefully analyzing the market. For better analysis of the stock market, investors often employ financial analysis of companies.
what is the future of Pi Network currency.DOT TECH
Β
The future of the Pi cryptocurrency is uncertain, and its success will depend on several factors. Pi is a relatively new cryptocurrency that aims to be user-friendly and accessible to a wide audience. Here are a few key considerations for its future:
Message: @Pi_vendor_247 on telegram if u want to sell PI COINS.
1. Mainnet Launch: As of my last knowledge update in January 2022, Pi was still in the testnet phase. Its success will depend on a successful transition to a mainnet, where actual transactions can take place.
2. User Adoption: Pi's success will be closely tied to user adoption. The more users who join the network and actively participate, the stronger the ecosystem can become.
3. Utility and Use Cases: For a cryptocurrency to thrive, it must offer utility and practical use cases. The Pi team has talked about various applications, including peer-to-peer transactions, smart contracts, and more. The development and implementation of these features will be essential.
4. Regulatory Environment: The regulatory environment for cryptocurrencies is evolving globally. How Pi navigates and complies with regulations in various jurisdictions will significantly impact its future.
5. Technology Development: The Pi network must continue to develop and improve its technology, security, and scalability to compete with established cryptocurrencies.
6. Community Engagement: The Pi community plays a critical role in its future. Engaged users can help build trust and grow the network.
7. Monetization and Sustainability: The Pi team's monetization strategy, such as fees, partnerships, or other revenue sources, will affect its long-term sustainability.
It's essential to approach Pi or any new cryptocurrency with caution and conduct due diligence. Cryptocurrency investments involve risks, and potential rewards can be uncertain. The success and future of Pi will depend on the collective efforts of its team, community, and the broader cryptocurrency market dynamics. It's advisable to stay updated on Pi's development and follow any updates from the official Pi Network website or announcements from the team.
how to swap pi coins to foreign currency withdrawable.DOT TECH
Β
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
where can I find a legit pi merchant onlineDOT TECH
Β
Yes. This is very easy what you need is a recommendation from someone who has successfully traded pi coins before with a merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi network coins and resell them to Investors looking forward to hold thousands of pi coins before the open mainnet.
I will leave the telegram contact of my personal pi merchant to trade with
@Pi_vendor_247
how to sell pi coins on Bitmart crypto exchangeDOT TECH
Β
Yes. Pi network coins can be exchanged but not on bitmart exchange. Because pi network is still in the enclosed mainnet. The only way pioneers are able to trade pi coins is by reselling the pi coins to pi verified merchants.
A verified merchant is someone who buys pi network coins and resell it to exchanges looking forward to hold till mainnet launch.
I will leave the telegram contact of my personal pi merchant to trade with.
@Pi_vendor_247
Introduction to Indian Financial System ()Avanish Goel
Β
The financial system of a country is an important tool for economic development of the country, as it helps in creation of wealth by linking savings with investments.
It facilitates the flow of funds form the households (savers) to business firms (investors) to aid in wealth creation and development of both the parties
Currently pi network is not tradable on binance or any other exchange because we are still in the enclosed mainnet.
Right now the only way to sell pi coins is by trading with a verified merchant.
What is a pi merchant?
A pi merchant is someone verified by pi network team and allowed to barter pi coins for goods and services.
Since pi network is not doing any pre-sale The only way exchanges like binance/huobi or crypto whales can get pi is by buying from miners. And a merchant stands in between the exchanges and the miners.
I will leave the telegram contact of my personal pi merchant. I and my friends has traded more than 6000pi coins successfully
Tele-gram
@Pi_vendor_247
Empowering the Unbanked: The Vital Role of NBFCs in Promoting Financial Inclu...Vighnesh Shashtri
Β
In India, financial inclusion remains a critical challenge, with a significant portion of the population still unbanked. Non-Banking Financial Companies (NBFCs) have emerged as key players in bridging this gap by providing financial services to those often overlooked by traditional banking institutions. This article delves into how NBFCs are fostering financial inclusion and empowering the unbanked.
1. Practical CVA and KVA Forum
London, 24th - 26th April 2017
Reasons behind FVA, MVA, KVA
Tommaso Gabbriellini Andrea Gigli
Head of Quants Head of Fixed Income and XVA
MPS Capital Services MPS Capital Services
2. Disclaimer
_______________________________________________________________________________________________________
These are presentation slides only. The information contained herein is for general guidance on matters of interest only and
does not constitute definitive advice nor is intended to be comprehensive.
All information and opinions included in this presentation are made as of the date of this presentation.
While every attempt has been made to ensure the accuracy of the information contained herein and such information has been
obtained from sources deemed to be reliable, neither MPS Capital Services, related entities or the directors, officers
and/or employees thereof (jointly, βMPSCS") is responsible for any errors or omissions, or for the results obtained from the use
of this information. All information in this presentation is provided "as is", with no guarantee of completeness, accuracy,
timeliness or of the results obtained from the use of this information, and without warranty of any kind, express or implied,
including, but not limited to warranties of fitness for a particular purpose. MPSCS does not assume any obligation whatsoever to
communicate any changes to this document or to update its contents. In no event will MPSCS be liable to you or anyone else for
any decision made or action taken in reliance on the information in this presentation or for any consequential, special or similar
damages, even if advised of the possibility of such damages.
This document represents the views of the authors alone, and not the views of MPSCS. You can use it at your own risk.
3. 3
Goals of the talk
β’ Using a multiperiodal structured model we are going to investigate
the rationale behind FVA, MVA and KVA
β’ The model represents a useful tool to understand the relations
between valuation adjustments, market parameters and regulatory
constraints
β’ Three main lessons can be learned from the model
β’ How to allocate capital to different business units
β’ How to manage funding strategies
β’ Hot to price banking products
4. 4
FVA, MVA, KVA
β’ MVA & FVA measure the impact on Equity due to IM and VM bankβs
obligations after entering derivatives contract, using debt to finance
those obligations.
β’ Regulatory requirements impose that the leverage of the balance
sheet remains below a predefined threshold ο KVA measures the
impact on the Equity as the bank fulfils the regulatory constraints
β’ In order to compensate shareholders for negative variations in the
Equity value a charge equal to MVA, FVA, KVA might be needed.
5. 5
The Model β Uniperiodal case
Assume:
- the risk meausure is the risk neutral one
- the bank will default if π΄(π) < πΏππ‘, where
- πΏππ‘is the amount of debt and interests to be paid and
- ππ‘ = 1 + ππ π‘,
- π π‘ is the funding spread set in t
- the risk free rate is zero.
The value of Equity in π‘ is
πΈπ‘ = πΌ π‘ πππ₯ π΄(π) β πΏππ‘, 0
The value of the Liabilities in π‘ is
πΌ π‘ πππ π΄(π), πΏππ‘ = πΏππ‘ β πΌ π‘ πππ₯ πΏππ‘ β π΄(π), 0
6. 6
The Model β Uniperiodal case
The spread π π‘ is set by the
creditor such that
πΏ β€ πΏππ‘ β πΌ π‘ πππ₯ πΏππ‘ β π΄(π), 0
the spread must be sufficient to remunerate the
risks
In the following we will assume that the creditor is always Β«fairΒ», i.e
the minimum spread is applied:
πΏ = πΏππ‘ β πΌ π‘ πππ₯ πΏππ‘ β π΄(π), 0
N.B.
if π π‘ is fair
πΈ(π‘) = π΄ π‘ β πΏ
Proof: πΈ(π‘) = π΄ π‘ β πΏππ‘ + πΌ π‘ πππ₯ πΏππ‘ β π΄(π), 0 = π΄ π‘ β πΏ
Put-Call Parity
7. 7
The Model β Uniperiodal case
What is the impact of a new investment on the equity value of the bank?
Assume at π‘+the bank issues new debt for funding a risk free asset whose
maturity is the same of the debt.
The fair spead on the new debt must be such that:
Fair spread
in π‘+
Assets Liabilities
πΈ(π‘+) = πΌ π‘+ max π΄(π) + πΆ β πΏππ‘ β βπΏππ‘+
, 0
πΆ = βπΏ = πΌ π‘ βπΏππ‘+
π π΄ π +πΆ>πΏππ‘+βπΏπ π‘+
+ π΄(π)
βπΏ
πΏ + βπΏ
π π΄(π)+πΆ<πΏππ‘+βπΏππ‘+
In case of default the assets will be used for a partial
reimburse proportionally to the face value of the liabilities
C doesnβt depend
upon t
8. 8
The Model β Uniperiodal case
π = π = 1
Note that:
β’ βπΏ = πΆ
β’ If π΄ π‘ β« C β ππ‘+ β ππ‘
Hence, the variation in the equity value is
πΌ π‘ max π΄(π) + πΆ(π) β πΏππ‘ β βπΏππ‘+, 0 β πΌ π‘ max π΄(π) β πΏππ‘, 0 =
β βπΆ β ππ π‘ β πΌ π‘ π π΄ π>πΏ π‘ ππ‘
This is the amount of money
shareholders requires in order to invest
borrowed money in a risk free asset
π‘+
Assets Liabilities
π΄(π‘+)
+ πΆ(π‘+)
πΏ π‘+ + βπΏ
Equity
πΌ π‘ πππ₯ π΄(π) + πΆ β πΏππ‘
β βπΏππ‘+
, 0
Assets Liabilities
π΄ π‘(π)
+ πΆ
πΏππ‘ + βπΏππ‘+
Equity
πππ₯ π΄ π + πΆ β πΏππ‘
β βπΏππ‘+
, 0
9. 9
The Model β Uniperiodal case
What if the asset is not risk free? There may be as well negative impacts
(Β«funding costsΒ») and positive ones (Β«funding benefitsΒ»), depending on
the volatility and correlation with the previous assets and its risk.
π΄ π‘ = 100
ππ΄ = 20%
πΏ = 90
π π‘ = 6.60%
ΞπΏ = π΄1(π‘+) = 10
10. 10
The Model β Multiperiodal case
In our multiperiodal settings we assume that the bank rolls its debt at its
maturity.
For the sake of simplicity, we analyze the case where the bank rolls its
debt just once
ππ‘ 2π 3π
πΏ πΏππ‘ πΏππ‘ ππ πΏππ‘ ππ π2π
ππ‘ 2π
πΏ πΏππ‘ πΏππ‘ ππ
11. 11
The Model β Multiperiodal case
ππ‘ 2π
πΏ πΏππ‘ πΏππ‘ ππ
We evaluate the equity by
means of the Β«tower properyΒ»
πΌ πΈ2π β±ππΈ(π‘) = πΌ πΌ πΈ2π β±π |β±π‘
Letβs look at the value of πΌ πΈ2π β±π in the following 2 cases
π΄ π β₯ πΏππ‘ π΄ π < πΏππ‘
The bank finance the debt +
interest at a new fair spread.
πΌ πΈ2π π΄ π > πΏππ‘ = π΄ π β πΏππ‘
The bank try to finance the debt
+ interest at a new fair spread,
but no one is willing to lend
moneyβ¦
πΌ πΈ2π π΄ π β€ πΏππ‘ = 0
Proof in the following slide
12. 12
The Model β Multiperiodal case
Why if π΄ π < πΏππ‘ no one is willing to lend money?
Letβs have a look at the fair value of the debt in the limit of an
infinite spread
lim
π πββ
πΌ π min π΄(2π), πΏππ‘ ππ = πΌ π π΄(2π) = π΄ π < πΏππ‘
The maximum fair value of the debt is always
lower than the amount to be financed!
πΌ πΈ2π β±π = max(A π β πΏππ‘, 0)Combining the two cases we have that
Therefore the equity can be priced as
πΈ π‘ = πΌ max(A π β πΏππ‘, 0) β±π‘
Exactly the same as in the uniperiodal setting
13. 13
The Model β Multiperiodal case
How is the FVA affected by the financing strategy of the bank?
Letβs consider the purchase at time π‘+ of a risk free asset (cash) whose
maturity is greater than π (the bond maturity), say 2π
Applying the same reasoning as before, the equity can be computed as
if the maturity of the newly purchased asset is the same as of the debt
πΈ(π‘+) = πΌ π‘+
max π΄(π) + πΆ β πΏππ‘ β βπΏππ‘+
, 0
The FVA is proportional to the financing Β«periodΒ», not
to the maturity of the asset, i.e. the following still
holds!
πΉππ΄ β βπΆ β ππ π‘ β πΌ π‘ π π΄ π>πΏππ‘
14. 14
An application for FVA/MVA
Suppose the bank enters in a back to back derivitave, one collateralized
and one not. Which is the impact on equity due to the funding of the
collateral (Initial Margin and Variation Margin) in the multiperiodal case?
RiskFree CTP
Bank
Collateralized
CTP
Initial Margin
Collateral
account
15. 15
MVA β Uniperiodal case
In this case we can treat the initial margin as a cash account whose exposure
varies (stochastically) through time.
-1.000.000
-
1.000.000
2.000.000
3.000.000
0 1 2 3 4 5
- we assume that the fraction of cash
coming back from the IM account is
used to buy back the bankβs
obbligations
- The maturity of the whole bank debt
equal to the derivativeβs one
- The IM is uncorrelated with the total
bank assets (πΌπ(π‘) βͺ π΄(π‘))
πππ΄ π’ππ β βπΌ π‘ π π΄ π>πΏππ‘
πΌπ π‘π π π‘(π‘π β π‘πβ1)
π:π‘ πβ‘π
π
IM(t) β Expected Initial Margin
16. 16
MVA β Uniperiodal case
In this case we can treat the initial margin as a cash account whose exposure
varies (stochastically) through time.
-1.000.000
-
1.000.000
2.000.000
3.000.000
0 1 2 3 4 5
- we assume that the fraction of cash
coming back from the IM account is
used to buy back the bankβs
obbligations
- The maturity of the whole bank debt
equal to the derivativeβs one
- The IM is uncorrelated with the total
bank assets (πΌπ(π‘) βͺ π΄(π‘))
πππ΄ π’ππ β βπΌ π‘ π π΄ π>πΏππ‘
πΌπ π‘π π π‘(π‘π β π‘πβ1)
π:π‘ πβ‘π
π
IM(t) β Expected Initial Margin
Spread never
resets
17. 17
MVA β Multiperiodal case
πππ΄ ππ’ππ‘ β βπΌ π‘ π(π΄ π1 > πΏ1 πΌπ π‘π π π‘(π‘π β π‘πβ1)
π:π‘ πβ‘π1
π
+
β πΌ π‘ π(π΄ ππ > πΏπ) (πΌπ π‘π β πΌπ ππβπ )π π πβ1
(π‘π β π‘πβ1)
π:π‘ πβ‘π π
π=1:π‘1β‘π πβ1
π:π πβ‘π
π=2
-1.000.000
-
1.000.000
2.000.000
3.000.000
0 1 2 3 4 5
Spread resets at each
refinancing date
Term similar to
uniperiodal, but up to π1π π π π π
π π π
π π π
π π π
19. 19
FVA for Collateral
πΉππ΄ ππ’ππ‘π β β πΌ π‘ π(π΄ ππ > πΏπ) (πΈπΈ π‘π β πΈπΈ ππβ1 )π π πβ1
(π‘π β π‘πβ1)
π:π‘ πβ‘π π
π=1:π‘1β‘π πβ1
π:π πβ‘π
π=1
Collateral
account
As for MVA, under the same assumptions, we treat the future exposure on the
collateral account as non stochastic and take instead the expected exposure.
πΉππ΄ π’ππ β βπΌ π‘ π π΄ π>πΏππ‘
πΈπΈ π‘π π π‘(π‘π β π‘πβ1)
π:π‘ πβ‘π
π
ππ½π¨ πππππ < ππ½π¨ πππ
(*)
(*) These are proxy formulas valid in the case of a derivative traded with payment in upfront.
20. 20
KVA - Regulatory obligations
Regulator requires that the balancesheet of any banks be respectful of
predetermined leverage ratios.
Those constraints have an impact on the Equity dynamics over time, on the ROE
of a bank, hence on the funding spread a bank can negotiate at the end of each
funding period.
What is the impact of the regulatory obbligations on the ALM strategy of the
bank? How does this affect the equity value (KVA)?
For the sake of simplicity, let the regulatory constraint be defined as
πΈππ’ππ‘π¦
π€π π΄π π ππ‘ππ
β₯ π₯%
where x% is the regulatory ratio.
21. 21
A case for FVA/KVA
In our model we assume:
β’ regulatory capital is the equity value given by the structural model
β’ bank operates on the regulatory threshold
β’ new capital will be invested proportionally into existing assets
β’ creditors have perfect knoweldge of the bankβs balance sheet and
the dynamics due to the regulatory obligations (i.e. capital raising)
22. 22
A case for FVA/KVA
This leads to the following equations problem
πΈ(π‘)
π€π΄(π‘)
=
πΈ(t+)
π€ 1 + πΌ π΄(t+) + π€1 π΄1(π‘+)
= π₯%
π΄1 = ΞπΏ = πΌ π‘+ π₯πΏππ‘+ π πππ‘βπππππ’ππ‘ππ +
π₯πΏ
πΏ+π₯πΏ
1 + πΌ π΄ π + π΄1 π πππππ’ππ‘ππ
πΌ π‘+ max(π΄1 + 1 + πΌ π΄ π β πΏππ‘ β ΞπΏππ‘+
, 0)
23. 23
A case for FVA/KVA
This leads to the following equations problem
πΈ(π‘)
π€π΄(π‘)
=
πΈ(t+)
π€ 1 + πΌ π΄(t+) + π€1 π΄1(π‘+)
= π₯%
π΄1 = ΞπΏ = πΌ π‘+ π₯πΏππ‘+ π πππ‘βπππππ’ππ‘ππ +
π₯πΏ
πΏ+π₯πΏ
1 + πΌ π΄ π + π΄1 π πππππ’ππ‘ππ
- πΌπ΄ π‘+ is the amount of cash raised in the capital increase and
reinvested in the existing asset
- π π‘+
in ππ‘ = 1 + ππ π‘+
is the fair spread on the debt issued to
purchase the new risky asset.
- π π‘+
, πΌ are the unknown variables which can be found by means of
a root find numerical algorithm.
πΌ π‘+ max(π΄1 + 1 + πΌ π΄ π β πΏππ‘ β ΞπΏππ‘+
, 0)
24. 24
FVA and KVA are tightly bounded and represents two sides of the same
coinβ¦
A case for FVA/KVA
The impact on shareholders who were long equity at t is FVA&KVA
FVA&KVA = πΈ π‘+ β πΈ π‘ + πΌπ΄ π‘+
πΈ π‘+ = πΌ π‘+ max( 1 + πΌ π΄ π β πΎ, 0) β πΈπ‘ + Ξπ΅π β πΌπ΄(π‘+)
KVA = πΈ π‘+ β πΈ π‘ + πΌπ΄ π‘+ β β(1 β Ξπ΅π) β πΌπ΄(π‘+)
To better understand the following numerical results it can be noted that
a capital increase has always a negative impact on existing shareholders
In fact
HINT
30. 30
Conclusions
β’ We showed that the FVA and MVA impact on Equity depends on the
rolling frequency of the debt and the ability of the market to price
properly the funding spread at the time the debt is rolled.
β’ Once regulatory constraints are introduced it not possible to separate
KVA and FVA components easily.
β’ The model defines an ALM Strategy: reduce the duration of liabilities
in periods of distressed conditions and increase the duration of
liabilities in period of flourishing conditions.
β’ The model defines the Pricing Policy: even if assets fair values do
not depend on bankβs funding cost, a pricing policy should also take
into account of potential losses on equity value due to funding level.
β’ The model defines a Transfer Price Policy: fund any business unit
accordingly to the marginal contribution to the total risk of the
Assets in the balance-sheet.
32. Questions?
Tommaso Gabbriellini Andrea Gigli
Head of Quants Head of Fixed Income and XVAs
MPS Capital Services MPS Capital Services
tommaso.gabbriellini@mpscs.it andrea.gigli@mpscs.it