Chapter 17 - Mathematical Framework for Integrating Market and Credit Risk

Abstract

This chapter provides the key mathematical concepts for integrating credit and interest rate risk. It discusses properties of the standard risk measures value at risk and expected shortfall, and provides concepts involved in analyzing the dependence structure of credit and interest rate risk. The chapter also emphasizes the importance of modeling the dependence of these two types of risk from a regulatory point of view. A way to assess the dependency of market and credit risk is to use the pricing formulas for credit-risky assets—such as corporate bonds—and analyze the theoretical pricing formulas under changing market risk factors. Furthermore, the chapter discusses the regulatory framework for integrating market and credit risk. There are two types of credit risks—direct and indirect risks. Direct credit risk is the risk of a failure by counterparty to deliver assets or funds when required to do so (the so-called default risk), or an increase of the probability that such a failure will occur in the future (the so-called downgrade risk). Indirect credit risk (also known as spread risk or credit dependent market risk) denotes the risk that the value of an asset held by the institute declines because of a change in the credit risk of some firm with which the institute has no direct dealings.