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Counterparty Credit Risk and Credit Value Adjustment: A Continuing Challenge for Global Financial Markets, 2nd Edition by Jon Gregory

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12.1 Definition of CVA

12.1.1 Why Pricing CVA is Not Easy

Pricing the credit risk for an instrument with one-way payments, such as a bond, is relatively straightforward – one simply needs to account for default when discounting the cash flows and add any default payment. However, many derivatives instruments have fixed, floating or contingent cash flows or payments that are made in both directions. This bilateral nature characterises credit exposure and makes the quantification of counterparty risk dramatically more difficult. Whilst this will become clear in the more technical pricing calculations, a simple explanation is provided in Figure 12.1, which compares a bond to a similar swap transaction. In the bond case a given cash flow is fully at risk (its value may be lost entirely) in the event of a default, whereas in the swap case only part of the cash flow will be at risk due to partial cancellation with opposing cash flows. The risk on the swap is clearly smaller due to this effect.3 However, the fraction of the swap cash flows that are indeed at risk are hard to determine as this depends on many factors such as yield curve shape, forward rates and volatilities.

Figure 12.1 Illustration of the complexity when pricing the credit (counterparty) risk on a derivative instrument such as a swap, compared with an instrument such as a bond. In the bond the cash flow circled is fully at risk (less recovery) in the event of default of the issuer but in the swap the equivalent cash ...

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