Coupling and Option Price Comparisons in a Jump-Diffusion
model
Vicky Henderson, David Hobson
Abstract
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 conves payoffs the option price is increasing in the 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 propsed in the literature as candidate pricing measures.
Our proods 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.
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