6
Counterparty Risk and Credit Valuation Adjustment
Hell is other people.
Jean-Paul Sartre

6.1 INTRODUCTION

Derivatives are marvelous as they enable hedging different specific risks. The result is a portfolio that may seem safer. However, this comes at the cost of replacing fairly common, well-understood risks with the exceptional risk that the counterparty may fail.
Counterparty credit risk is defined as the risk that a counterparty in an over the counter (OTC) derivative transaction will default prior to the expiration of the contract and hence will be unable to make all contractual payments. Credit value adjustment is the price of counterparty credit risk. It can be calculated as the risk-neutral expectation of the discounted loss over the life of the transaction. The exposure to a counterparty at any future time is the loss experienced where the counterparty defaults at that time, assuming zero recovery rate. In this chapter, we address the problem of credit valuation adjustment (CVA) for a credit default swap (CDS). As an example, we consider a CDS intermediation business case.
A typical transaction in the CDS intermediation business is built as follows. On the one hand, the intermediator (I) sells (collateralized) protection on a reference entity to a collateralized counterparty (CC). On the other hand, the intermediator buys protection on the same reference entity for a noncollateralized counterparty (NCC) to hedge this position. Such a transaction has an asymmetric ...

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