Hedging credit risk using equity derivatives
Date
2008-06-30T11:35:38Z
Authors
Teixeira, Paul
Journal Title
Journal ISSN
Volume Title
Publisher
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.