Pricing and Hedging Options on Defaultable Assets
by Michel H. Vellekoop of the University of Twente,
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 extra uncertain factor, and there are therefore too few assets to construct a hedge against all sources of uncertainty. In this paper 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-systematic 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 other 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.