1. Counterparty Credit Risk in Derivatives
Chapter 17
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

2. Clearing Arrangements for OTC Derivatives (Figure 17.2, page 381)
Bilateral clearing: usually governed by an ISDA Master agreement
Central clearing: a central clearing party (CCP) stands between the two sides
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

3. Regulations
Standard OTC transactions must be cleared through a CCP (some exceptions)
Nonstandard OTC transactions continue to be cleared bilaterally, but with much higher capital charges
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

4. Central Clearing: Role of CCP (Figure 17.1, page 380)
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

5. Key Questions How many CCPs Will there be interoperability?
Will benefits of netting increase or decrease?
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

6. Simple Example: 3 market participants; 2 product types (Figure 17
Simple Example: 3 market participants; 2 product types (Figure 17.3, page 382)
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

7. Bilateral Clearing:The ISDA Master Agreement
One important feature is netting
This states that all transactions with the counterparty are considered to be a single transaction in the case of early termination and for the purposes of posting collateral
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

8. Events of Default and Early Termination
Declaration of bankruptcy
Failure to make payments on derivatives as they are due
Failure to provide collateral when it is due
The non-defaulting party has the right to declare an early termination event a few days after an event of default if there has been no resolution of outstanding issues
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

9. Collateral Arrangements
The credit support annex (CSA) of the ISDA Master Agreement specifies
Threshold
Independent Amount
Minimum Transfer Amount Eligible Securities and Currencies
Haircuts
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

10. Possible ISDA Clause: Downgrade Triggers
Specify that in the event of a downgrade the counterparty has certain rights.
It might specify that the counterparty can terminate outstanding transactions or that the counterparty can require collateral
In AIG’s case counterparties could require collateral in the event of a downgrade below AA. This necessitated a huge government bailout.
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

11. CVA
Credit value adjustment (CVA) is the amount by which a dealer must reduce the value of transactions because of counterparty default risk
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

12. The CVA Calculation ……………… ……………… ……………… Time t1 t2 t3 t4 tn=T q1 q2t1 t2 t3 t4
tn=T
………………
Default probability q1 q2 q3 q4 qn
……………… v1 v2 v3 v4
PV of net exposure vn
where R is the recovery rate
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

13. CVA continued
The default probabilities (i.e., the qi’s) are calculated from credit spreads
The PV of the net exposure is calculated using Monte Carlo simulation. Random paths are chosen for all the market variables underlying the derivatives and the net exposure is calculated at the mid point of each time interval. (These are the “default times”
The vi is the present value of the average net exposure at the ith default time
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

14. Calculation of Net Exposure
If no collateralization the net exposure is the maximum of the value of the derivatives and zero
If collateral is posted we assume that there is a “cure period” (= c days) immediately before a default during which collateral is not posted.
On each Monte Carlo trial we must calculate the value of the portfolio c days before each default time
This determines the collateral available at the default time
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

15. Incremental CVA
Results from Monte Carlo are stored so that the incremental impact of a new trade can be calculated without simulating all the other trades.
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

16. CVA Risk
The CVA for a counterparty can be regarded as a complex derivative
Increasingly dealers are managing it like any other derivative
Two sources of risk:
Changes in counterparty spreads
Changes in market variables underlying the portfolio
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

17. Basel III (2010)
Basel III requires CVA risk arising from a parallel shift in the term structure of counterparty credit spreads to be included in the calculation of capital for market risk
It does not require banks to include CVA risk arising from the underlying market variables
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

18. Wrong Way/Right Way Risk
Simplest assumption is that probability of default qi is independent of net exposure vi.
Wrong-way risk occurs when qi is positively dependent on vi
Right-way risk occurs when qi is negatively dependent on vi
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

19. Examples Wrong-way risk typically occurs when
Counterparty is selling credit protection
Counterparty is a hedge fund taking a big speculative positions
Right-way risk typically occurs when
Counterparty is buying credit protection
Counterparty is partially hedging a major exposure
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

20. Problems in Estimating Wrong Way/Right Way Risk
Knowing trades counterparty is doing with other dealers
Knowing how different market variables influence the fortunes of the counterparty
Do counterparties become more likely to default when interest rates are high or low? The evidence is mixed and so we do not know whether receiving or paying fixed generates wrong way risk
Even when there appears to be right-way risk liquidity problems can lead to a company being unable to post collateral (e.g Ashanti)
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

21. Allowing for Wrong-Way risk
One common approach is to use the “alpha” multiplier to increase the v’s
Estimates of 1.07 to 1.1 for alpha obtained from banks
Basel II sets alpha equal to 1.4 or allows banks to use their own models, with a floor of 1.2
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

22. DVA (more recent and more controversial)
Debit (or debt) value adjustment (DVA) is an estimate of the cost to the counterparty of a default by the dealer
Same formulas apply except that v is counterparty’s exposure to dealer and q is dealer’s probability of default
Accounting value of transactions with counterparty = No default value – CVA + DVA
Copyright 2011 © John Hull, Joseph L. Rotman School of Management, University of Toronto

23. DVA continued
What happens to the reported value of transactions as dealer’s credit spread increases?
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

24. Expected Exposure on Pair of Offsetting Interest Rate Swaps and a Pair of Offsetting Currency Swaps (No collateral) (Figure 17.2, page )
Exposure
Currency swaps
Interest Rate Swaps
Maturity
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

25. Interest Rate vs Currency Swaps
The qi’s are the same for both
The vi’s for an interest rate swap are on average much less than the vi’s for a currency swap
The expected cost of defaults on a currency swap is therefore greater.
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

26. Simple Example: Single transaction always has positive value to dealer
CVA has the effect of multiplying value of transaction by e-sT where s is spread between T-year bond issued by counterparty and risk-free T-year bond
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

27. Example 17.1 (page 391)
A 2-year option sold by a counterparty to the dealer has a Black-Scholes value of $3
Assume a 2 year zero coupon bond issued by the counterparty has a yield of 1.5% greater than the risk free rate
If there is no collateral and there are no other transactions between the parties, value of option is 3e-0.015×2=2.91
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012

28. Dealer Has Single Long Forward with Counterparty (page 392)
For a long forward contract that matures at time T the present value of the exposure at time ti is
F0 is the forward price today, K is the delivery price, s is the volatility of the forward price, T is the time to maturity of the forward contract, and r is the risk-free rate
Risk Management and Financial Institutions 3e, Chapter 17, Copyright © John C. Hull 2012