Pricing and Hedging Options on Defaultable Assets

Abstract

In general contingent claims on assets which may default during the duration of the contract cannot be priced and hedged consistently. This is due to the fact that the possibility of a default event brings in an uncertain factor and there are therefore too few assets to construct a hedge against all sources of uncertainty. In this papaer we show that consistent pricing and hedging is still possible if we assume that 1) we can estimate the size of the loss in value (as a percentage) upon default and 2) default is the only non-systemic risk factor involved. Moreover we show that the resulting formulas for prices and hedges do not depend on the intensity of the default process but on a new riskfree intensity which is an explicit function of other parameters in the model in contrast to most models. We derive a simple tree method to implement the methodology that is proposed and show how other pricing methods for claims on defaultable assets are linked to our method.

Keywords: Hedging, Default, Jump-Diffusion

JEL Classification: C00