Coupling and Option Price Comparisons in a Jump Diffusion Model
Dr David Hobson, Department of Mathematical Sciences, University of Bath

In this paper we examine the dependence of option prices in a general jump-diffusion model on the choice of martingale pricing measure. Since the model is incomplete there are many equivalent martingale measures. Each of these measures corresponds to a choice for the market price of diffusion risk and the market price of jump risk. Our main result is to show that for convex payoffs the option price is increasing in the jump-risk parameter. We apply this result to deduce general inequalities comparing the prices of contingent claims under various martingale measures which have been proposed in the literature as candidate pricing measures.

Our proofs are based on couplings of stochastic processes. If there is only one possible jump size then we are able to utilize a second coupling to extend our results to include stochastic jump intensities.