Chapter 7

Pricing CounterpartyCredit Risk, I

“Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.“

Albert Einstein (1879–1955)

In Chapters 4 and 5 we discussed how to quantify credit exposure, whilst Chapter 6 concerned default probability. Now we proceed to combine these two components in order to address the pricing of counterparty credit risk. We will see that under certain commonly made assumptions it is relatively simple to combine default probabilities and exposures to arrive at an appropriate price for counterparty risk.

Accurate pricing of counterparty risk involves attaching a value to the risk of all outstanding positions with a given counterparty. This is important in the reporting of accurate earnings information and incentivising trading desks and businesses to trade appropriately. If counterparty risk pricing is combined with a systematic charging of new transactions, then it will generate funds that can be used to absorb potential losses in the event a counterparty defaults. Counterparty risk charges may also be associated with hedging costs in relation to credit risk aspects.

There have been many models proposed for pricing counterparty risk, which mostly cover the “classic” instrument types. For example, Sorenson and Bollier (1994), Jarrow and Turnbull (1992, 1995, 1997), Duffie and Huang (1996) and Brigo and Masetti (2005a) describe reduced-form models for counterparty risk and focus mainly on interest rate and foreign ...

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