Throughout this presentation, you’ll learn:  General risks faced by banking institutions on the derivatives markets.  How the main banking/accounting regulatory bodies’ actions are framing the banking industry (SA-CCR, IFRS 13, etc.).  The origins of xVAs and how they are challenging the so-far asset valuation theory.  The quantification techniques of CVA components.  The existing CVA risk mitigation techniques.

1. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
xVAs: The Post–Lehman Derivatives Valuation
Adjustments
Alex Kouam 1
Master of Science International Banking and Finance (Strathclyde Business School)
Specialized Master Quantitative Finance (EMLYON Business School)
31st August 2017
1
Unauthorised use prohibited Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

2. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Outline I
1 General Market Business Activties Risks
2 Treasurer Activities
3 Banking Regulation
Stakeholders, Geographical Scope and Roles
Current EU Regulation
4 xVAs
5 CVA
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
6 CVA Risk Mitigation Techniques
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

3. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Outline II
Collateralization
Netting Agreements
Hedging
7 FVA
8 ColVA
9 KVA
10 Challenges brought up by the xVAs
11 Conclusion
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

4. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
General Market Business Activties Risks
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

5. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
General Market Business Activties Risks I
Credit Risk stands for the risk of a counterparty defaulting on
payment obligations
E.g.: Enron (2001) declared a loss of $1 billion in October 2001 with
revalued libabilities of over $60 billion at the bankruptcy filing.
Liquidity Risk (Funding) is the risk that the cost of funding
becomes higher, up to the extreme case when raising funds become
impossible.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

6. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
General Market Business Activties Risks II
E.g. Northern Rock (2007) were unable to sell securitized loans to
secure funding.
Market Risk is the risk of adverse deviations from the
mark–to–market value of the trading portfolio, due to market
movements, during the period required to liquidate the transactions.
E.g. JP Morgan (2012) incurred mark–to–market losses of $6.2 billion
on the Synthetic Credit Portfolio
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

7. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
General Market Business Activties Risks III
Operational Risk outcomes from direct or indirect loss resulting from
inadequate or failed internal processes, people and systems or from
external events.
E.g. Barings (1995), Soci´et´e G´en´erale (2008) and UBS (2011) lost
respectively $1.4 billion, e4.9 billion and £1.4 billion because of rogue
traders who managed to deceive internal control systems.
Counterparty credit risk is the risk that the counterparty to a
financial contract will default prior to the expiration of the contract
and will not make the payments required by the contract.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

8. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
General Market Business Activties Risks IV
E.g. American International Group (AIG) which wrote more than
$500bn of Credit Default Swaps contracts and was unable to post
further collateral when the turmoil in the housing market reached its
climax.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

9. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Treasurer Activities
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

10. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Activities of a Treasurer
Secure term funding.
Ensure liquidity for derivatives trading.
Transferring these costs to the business.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

11. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Stakeholders, Geographical Scope and Roles
Current EU Regulation
Banking Regulation
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

12. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Stakeholders, Geographical Scope and Roles
Current EU Regulation
Missions
In a nutshell, banking regulation aims to:
Guarantee the financial system resilience and integrity, the economy’s
lifeblood and,
Protect financial products’ consumers, in particular to maintain a high
level of confidence in the system.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

13. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Stakeholders, Geographical Scope and Roles
Current EU Regulation
Table
Institutions Geographical Coverage Roles
G20 World • The G20 set top priorities
FSB • FSB makes those priorities operational
Basel Committee • The Basel Committe publishes
these recommendations
European Parliament Europe • The Euopean institutions adapt
European Commission these recommendations to the
EBA European context through
Capital Requirements Regulation
(CRR) and Capital Requirements
Directive (CRD)
French Parliament France •They adopt the EU agencies directives
ACPR with respect to the French law
CCLRF
Table: Main Regulatory BodiesAlex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

14. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Stakeholders, Geographical Scope and Roles
Current EU Regulation
Current EU Regulation
Issue Key Points
SA–CCR • CEM and SM are replaced by
SA–CCR
• A modified Original Exposure
method is retained
CVA •a failure to meet FRTB–CVA
requirements will lead to a
fallback to the BA–CVA
(higher capital requirements)
Table: EC CRR Amendments
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

15. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
xVAs
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

16. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
xVAs: Overview
Adjustment Target Objectives Market driver(s)
CVA Uncollateralised derivatives Anticipates on future costs IFRS 13
caused by the counterparty’s Basel 3
creditworthiness deterioration
FVA Uncollateralised derivatives Captures the funding NSFR, LCR
costs/gains of TLAC (G–SIBs)
derivatives above the”risk–free” IFRS 13 (DVA)
rate.
ColVA Collateralised derivatives Captures cost of funding a Cheapest to deliver
derivative position at collateral
new ”risk free” rate
KVA All the derivatives book Aims to capture cost of holding regulatory CVA/CCR Capital Charge
capital as a result of the derivative position Leverage Ratio, Market Risk
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

17. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CVA
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

18. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CCR: Origins I
Through deposits, investments, OTC derivatives or securities
financing transactions, the treasurer will create credit exposure.
This credit exposure is defined as the cost of replacing the transaction
if the counterparty defaults (assuming no recovery value).
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

19. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CCR: Specific Properties I
Unlike other forms of credit risk, this credit exposure features asymmetric
characterisrics:
If the company is owed money and the counterparty defaults then the
company will incur a loss whereas
In the reverse, the company will not gain from the default by being
released from their liability.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

20. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Some Credit Exposures Metrics I
In order to efficiently manage her credit exposure, our treasurer needs
to build metrics which provides answers to the following questions:
What is the maximum loss if the counterparty defaults now?
What could be the loss if the counterparty defaults at some point in the
future?
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

21. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Some Credit Exposures Metrics II
If we define the Mark–to–Market (MtM) as the value of a transaction
at some point in the future, our treasurer could summarize her credit
exposure using the three following metrics:
Potential Future Exposure (PFE): attempts to answer the first
question. Although, the PFE is sometimes referred as the VaR
analogue for CCR, it differs from this latter not only on the focus of
the exposure signs but also usually covers much longer periods than
the VaR. Mathematically, PFEα is:
PFEα(t) = max (MtM (0; t) , 0)
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

22. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Some Credit Exposures Metrics III
Expected Exposure (EE): represents the expected amount to be lost
if the counterparty defaults. Mathematically:
EE(t) = E [max (V (t) , 0)]
=
∞
0
xdF[0,t](x)
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

23. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Some Credit Exposures Metrics IV
Expected Positive Exposure (EPE): Given the lenghty term of
derivatives, the EPE will measure EE across the time. Mathematically,
EPE(0; t) = E
1
t
t
0
EE(s)ds
=
1
t
t
0
EE(s)ds
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

24. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Exposure Metrics: Illustration I
Parameters
µ(%) σ(%) α(%) EPE
0 10 95 8,529
Table: Exposure of a Forward Contract
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

25. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Exposure Metrics: Illustration II
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

26. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CCR: Quantification aims
trade approval by comparing against credit lines (PFE).
pricing (and hedging) CCR.
calculating economic and regulatory capital.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

27. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CCR: Quantification Methods I
We have two main methods to quantify CCR:
1 Mark–to–market + add–ons: Take the positive MtM and add a
component. That component depends on:
time horizon (larger add–on for long–term transaction)
volatility of the underlying asset class (Higher volatility for FX and
commodities)
the nature of the underlying transaction(s) (higher add–on for
non–G10 currencies.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

28. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CCR: Quantification Methods II
2 Monte–Carlo simulation: more complex and time–consuming but
can cope with add–on’s ignored complexities such as transaction
specifics, path dependency, etc. . . .
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

29. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CCR Quantification: Monte–Carlo simulation (MCS) I
The steps for a MCS quantification are:
1 Factor Choice: Select the risk factor(s) that influence the exposure
of the transaction. E.g. Spot interest rate, FX, etc. . .
2 Scenario Generation: Generate scenario of risk factors in which each
scenario represents a joint realisation of risk factors at various point in
time.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

30. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CCR Quantification: Monte–Carlo simulation (MCS) II
3 Revaluation: Use the values generated at step 2 to revalue the
position at each point in time in the future.
4 Aggregation: Aggregate those values up to the netting set. This
step requires a knowledge of the netting agreements.
5 Post–Processing We go through each exposure path, determine at
each point how much the exposure would be collateralized and apply.
6 Extraction of Statistics: At this step, you can easily extract the
metrics that we did cover earlier.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

31. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CCR Quantification: Monte–Carlo simulation (MCS) III
Roll–off risk
Exposures will be calculated at only discrete time points and we can
miss any key area.
Incorporate the critical points where exposures change significantly
into the time grid.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

32. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
PD I
We saw earlier that exposure depends on the counterparty’s default,
then an assessment of the default probability term structure is also
crucial for risk manangement.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

33. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
PD II
Our treasurer needs to consider two aspects:
What is the probability of the counterparty defaulting in a certain time
horizon?
What is the probability of the counterparty suffering a decline in credit
quality over a certain time horizon?
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

34. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
PD: Definition I
The probability of default between two future dates u1 and u2, where
u1 ≤ u2, is:
q (u1, u2) = S (u1) − S (u2)
= F (u2) − F (u1)
where, S (u) is the probability of no default prior to a certain time u and
F (u) = 1 − S (u) is the cumulative probability of default prior to a certain
time u
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

35. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
CDS Illustration on a single reference entity
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

36. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Market–Implied Probabilities
Here the default probability is worked out by calibrating a hazard rate h
which defines the probability of default in a small interval dt
S (u) = exp (−hu)
where h ≈ XCDS
(1−δ)
XCDS is the CDS premium and δ is constant recovery rate.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

37. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Intersection Methodology I
The EBA (2012) has been laying down rules as part of CRD IV about
the way illiquid counterparty’s spreads should be proxied.
The Intersection Methodology consists of aggregating data across
the relevant rating, region, sector sub–categories. Mathematically:
Sproxy
i =
1
N
N
j=1
S (j)
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

38. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Intersection Methodology II
Where N ≥ 1 is the number of liquid names in the same rating,
region, sector sub–categories as obligor i and
S (j) is their spread levels.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

39. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Historical Probabilities
This consist of using the ratings from the prominent rating agencies
(Standard & Poor’s, Moody’s, Fitch) to predict future default likelihood
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

40. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
PD: Gap between Historical and Market–implied
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

41. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Equity–based approach I
Merton (1974) states that default happens by the time that a firm’s asset value (Vt )
falls beneath its debt’s book value (B).
Assumptions:
Market is perfect (no dividends, no taxes,...).
Firm’s asset value follows a geometric Brownian motion.
The single class of debt (B) maturity matches the time period under scrutiny
(usually one year).
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

42. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Equity–based approach II
Firm’s capital structure is only made up of equity (Et ) and a zero–coupon bond
(B).
Pt = P [VT < B]
...
= Φ −
log Vt
B
+ α − 1
2
σ2
V (T − t)
σV
√
T − t
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

43. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
LGD
The loss given default (LGD) measures the percentage of all exposure at
the time of default that cannot be recovered
LGD is related to the recovery rate(RR) using the following relationship:
LGS = 1 − RR where RR is usually assumed as a constant
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

44. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
LGD: Equity–based approach
But if we aim to be consistent with the PD’s equity–based approach, we can work out
the implied RR as such:
E
VT
B
|VT < B =
1
B
E [VT |VT < B]
...
=
V0
B
exp (αT)
Φ −
log
V0
B
+ α+
σ2
V
2
T
σV
√
T
Φ −
log
V0
B
+ α−
σ2
V
2
T
σV
√
T
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

45. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Counterparty Credit Risk (CCR)
Probability of Default (PD)
Loss Given Default (LGD)
Pricing CVA: No Wrong–way Risk
CVA is usually tagged as the price of CCR because the move to either enter
into a new transaction with a counterparty depends upon whether or not
this latter will be profitable once you ”price in” its CCR. Mathematically:
˜V (t, T) = V (t, T) − EQ
(1 − δ) I (τ ≤ T) V (τ, T)+ β(s)
β(τ)
CVA
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

46. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
CVA Risk Mitigation Techniques
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

47. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
CCR: Controlling Techniques I
The methods for doing this predominantly focus on reducing current credit
exposure and potential future exposure.
Default–remote entities: The use of an institution or vehicle with a
low underlying default probability. E.g. SPV, CCP.
Termination events: provides the opportunity to terminate a
transaction at some point(s) between inception and maturity date.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

48. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
CCR: Controlling Techniques II
Netting: allows two parties to net a set of positions(explicitly covered
by the netting agreement) in the event of default of one of them.
Close–out: allows the termination of all contracts between the
insolvent and a solvent counterparty without waiting for the
bankruptcy to be finalised.
Collateralisation: The agreement that cash or other securities will
be posted as a guarantee against an exposure according to
pre–defined parameters.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

49. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Collateralization: Aims I
In the aftermath of the GFC, collateral use to reduce CCR has
substantially increased.
According to ISDA (2010), more than 70% of all OTC derivatives
transactions were collateralized. The aims of collateral management
are:
Reduce credit exposure so as to be able to do more business.
Enables ones to trade with a particular counterparty. For instance,
restricted rating may not allow uncollateralized transactions,
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

50. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Collateralization: Aims II
Reduce capital requirement
To give more competitive CCR’s pricing.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

51. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Collateralization: The Basics
In a swap transaction between parties A and B, party A makes a MtM
profit whilst party B makes a corresponding MtM loss.
Party B posts some form of collateral (cash or other securities) to
party A to cover against party A’s positive MtM.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

52. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Types of collateral I
Cash
Government securities
Government agency securities (e.g. Fannie Mae/Freddie Mac).
Mortgage–backed securities (MBSs).
Corporate bonds/ commercial paper.
Letters of credit and guarantees.
equity
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

53. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Composition of a Collateral Agreement I
Base currency
Type of agreement (one–way or two–way): Is one or both that have
to post collateral in the case of negative MtM?
Quantification of parameters: Independent amount, threshold,etc. . .
Eligible collateral to be posted alongside with applicable haircuts.
Timings regarding the delivery of collateral (margin call frequency,
notification times and delivery periods)
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

54. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Composition of a Collateral Agreement II
Interest rate payables on cash collateral.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

55. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Collateralization: The Mechanics I
The elements covered by a typical Credit Support Annex (CSA) are:
Independent Amount(IA): or initial margin corresponds to a
quantity of collateral that is posted upfront and is independent of any
subsequent collateral. It is typically held as a cushion against the risk
that the market value of a transaction may fall substantially in a short
space of time (”Gap risk”).
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

56. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Collateralization: The Mechanics II
Margin call frequency: refers to the periodic timescale with which
collateral may be called and returned.
Threshold: is a level of exposure below which collateral will not be
called and hence any exposure within the threshold will be
uncollateralised.
Minimum Transfer amount (MTA): is the smallest amount of
collateral that can be transferred and is used to avoid cumbersome
transfer of insignificant amounts of collateral.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

57. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Collateralization: The Mechanics III
Rounding: A collateral call or return will always be rounded to a
certain lot size to avoid unnecessarily small amounts.
Haircuts: are discount applied to the value of collateral to account
for the fact that its value may deteriorate over time. These discounts
are applied on all collateral excluding cash.
Coupons and interest payments: Interest will be typically paid on
cash collateral at an overnight rate (EONIA, Fed Funds,etc. . . )
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

58. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Risks of Collateralization I
Although collateralisation has the benefits of undermining the underlying
market risk, this mitigation technique creates other risk such as:
1 Operational Risk: missed collateral calls, failed deliveries, unsuitable
IT systems, etc. . . .
2 Default Risk: Default relating to a security posted as collateral would
clearly reduce the value of that collateral substantially and the applied
haircut is very unlikely to cover such an event
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

59. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Risks of Collateralization II
3 FX Risk: When two counterparties do not have the same local
currency, one of them will have to take FX risk linked to the collateral
posted.
4 Liquidation Risk: risk that by liquidating an amount of a security that
is large compared with the volume traded in that security.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

60. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Netting Agreements
A netting agreement is a legally binding contract that allows
aggregation of transactions if either of counterparty defaults.
Across netting sets, exposure will always be positive, whereas within a
netting set, MtM values can be added.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

61. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
The drawbacks of Netting
Netting is heavily dependent of the type of underlying involved.
Legal issues regarding the enforceability of netting could undermine
this latter’s benefits in the case that trades are booked with different
legal entities across different regions.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

62. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Hedging
This step involves many different market variables and the potential
linkage between them.
Hedging will be far from perfect and the most pragmatic solution is to
identify the key compoents of CVA that can and should be hedged, as
well as those that cannot.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

63. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Hedging CVA: Not a Risk–Neutral Problem I
Although Black–Scholes managed to create the link between the price of
an option and a dynamic hedging strategy, some important point to be
stressed when hedging CVA:
Variables: CVA usually embeds several underlying risk factors
(interest rates, FX rates and credit spreads)
Cross–dependency: CVA is a complex credit hybrid payoff because
the dependency between underlying factors might be non–trivial.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

64. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Hedging CVA: Not a Risk–Neutral Problem II
Term Structure: CCR is characterised by long–term trades and
hedging one underlying risk factor sensitive to term structure may
involve position in hedgings with different maturity dates.
Inability to hedge some variables: Some impactful parameters (e.g.
credit parameters) to the CVA cannot be hedged either because there
is no existence of an instrument with the required sensitivity or the
hedging costs are high.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

65. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateralization
Netting Agreements
Hedging
Hedging CVA: Not a Risk–Neutral Problem III
Lack of arbitrage: In order for an arbitrageur to take advantage of a
CCR mispricing error of an institution A on B, they need to trade with
institution A a contract referencing the credit quality of institution B.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

66. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
FVA
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

67. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Fund Valuation Adjustment I
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

68. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Fund Valuation Adjustment II
Since the outbreak of the GFC, there is a stark divergence between
the interbank lending/offering rate and the overnight rate.
FVA is divided into two components adjustments:
Funding Benefit Adjustment (FBA): arises when a bank acquires a
derivative in a liability position(negative MtM).
Funding Cost Adjustment (FCA): arises when a bank acquires a
derivative in an asset position(positive MtM).
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

69. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
ColVA
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

70. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateral Value Adjustment I
The choice of collateral impacts the discounting curve.
There’s a lot of optionality embedded in the current CSA agreements
where there allow collateral in cash or Treasury or corporate bonds in
various currencies.
It’s really important for the bank or the firm to identify which one will
be the cheapest to post because by minimizing the funding rate
(sborrow - spost) on collateral they will maximize their profit.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

71. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateral Value Adjustment II
Almost each agreement is unique (choice of collateral currency,
different thresholds, etc. . . ), then you will need to identify the
cheapest collateral possible for each trade.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

72. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Collateral Value Adjustment III
Not every cheapest to deliver collateral is the optimal choice and the right
approach before making a final choice should look the following aspects:
Analyze the funding rate.
Look at the available pool of assets.
Is cheaper to source new collateral or use existing one?
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

73. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
KVA
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

74. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
KVA: Origins
The subsequent capital requirements in the aftermath of the GFC set
substantial holding amounts of capital for derivative positions. And its
more punitive for non–centrally cleared derivatives.
Other xVAs focus on adjusting expected costs (losses) over the
lifetime of a transaction at present time.
But unexpected costs will also arise during the lifetime of the
transaction and KVA aims to capture it.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

75. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Definition and Drivers
KVA can be defined as the present value of the future capital costs
due to the various charges
KVA depends upon:
Counterparty nature: CCPs and many non–financials are exempt from
CVA charge and/or have lower CCR.
CSA(via CVA risk charge and credit exposure). Collateralization and
Initial Margin reduce CCR.
Availability of CDS protection to reduce CVA risk charge.
Diffusion models, measures, calibration.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

76. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Challenges brought up by the xVAs
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

77. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
CDS Gross Notional Graph
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

78. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Challenges brought up by the xVAs
How do I get the Credit curve of my counterparty? The CDS market
has not been very liquid over the last few years especially for
counterparty whose spreads is not traded on the market.
The cheapest to deliver pricing is very challenging.
FVA: What’s my funding cost (short, medium, long).
KVA: What return of capital do I want? Do we have to include tax
efficiency?
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

79. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Conclusion
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments

80. General Market Business Activties Risks
Treasurer Activities
Banking Regulation
xVAs
CVA
CVA Risk Mitigation Techniques
FVA
ColVA
KVA
Challenges brought up by the xVAs
Conclusion
Conclusion
Key Takeaways
The GFC abated the longstanding theory of a unique price for every
asset and ever since, derivative pricing depends upon the
characteristics of the trade.
Alignment of front office, accounting and regulation are still in the
flux (CVA/DVA). Banks who still used historical data and / or
internally–produced models parameters must design their processes
around market–implied parameters.
Alex Kouam xVAs: The Post–Lehman Derivatives Valuation Adjustments