In this chapter we show how to handle counterparty risk when pricing some basic financial products. In particular we are analyzing in detail counterparty-risk (or Default-risk) Interest Rate
Swaps and counterparty-risk equity return
swaps. The reason to introduce counterparty risk when evaluating a contract is linked to the fact that many financial contracts are traded over the counter (OTC), so that the credit quality of the counterparty can be important. This is particularly appropriated when thinking of the different defaults experienced by some important companies during the last years. Also, regulatory issues related to the Basel II framework encourage the inclusion of counterparty risk into valuation. We face the problem from the viewpoint of a safe (default-free) counterparty entering a financial contract with another counterparty that has a positive probability of defaulting before the
maturity of the contract itself. We are assuming there are no guarantees in place (such as for example collateral). When investing in default risky assets we require a risk premium as a reward for assuming the default risk. If we think, for example, of a corporate bond, we know that the yield is higher than the corresponding yield of an equivalent treasury bond, and this difference is usually called credit
spread. The (positive) credit
spread implies a lower price for the bond when compared to default free bonds. This is a typical feature of every asset: The value of a generic
claim traded with a counterparty subject to default risk is always smaller than the value of the same
claim traded with a counterparty having a null default probability.
[Authors: Damiano Brigo and Massimo Masetti / A refined version is "Risk Neutral Pricing of Counterparty Risk, in: Pykhtin, M. (Editor), Counterparty Credit Risk Modeling: Risk Management, Pricing and Regulation. Risk Books, London", 2005.]