David Hobson, Vicky Henderson
In this talk we examine the dependence of option prices in a 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. The main result is 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 pricing measures which have been proposed in the literature as candidate pricing measures.
The proofs are based on couplings of stochastic processes. If there is only one possible jump size then there is a second coupling which can be used to extend the results to include stochastic jump intensities.