Hedging credit risk using equity derivatives

Abstract

Equity and credit markets are often treated as independent markets. In this dissertation our objec- tive is to hedge a position in a credit default swap with either shares or share options. Structural models enable us to link credit risk to equity risk via the ¯rm's asset value. With an extended version of the seminal Merton (1974) structural model, we value credit default swaps, shares and share options using arbitrage pricing theory. Since we are interested in hedging the change in value of a credit default swap dynamically, we use a jump-di®usion model for the ¯rm's asset value in order to model the short term credit risk dynamics more accurately. Our mathematical model does not admit an explicit solutions for credit default swaps, shares and share options, thus we use a Brownian Bridge Monte Carlo procedure to value these ¯nancial products and to compute the delta hedge ratios. These delta hedge ratios measure the sensitivity of the value of a credit default swap with respect to either share or European share option prices. We apply these delta hedge ratios to simulated and market data, to test our hedging objective. The hedge performs well for the simulated data for both cases where the hedging instrument is either shares or share options. The hedging results with market data suggests that we are able to hedge the value of a credit default swap with shares, however it is more di±cult with share options.