Coupling and Option Price Comparisons in a Jump-Diffusion model
AbstractIn 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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Bibliographic InfoPaper provided by Oxford Financial Research Centre in its series OFRC Working Papers Series with number 2002mf01.
Date of creation: 2002
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2003-08-31 (All new papers)
- NEP-FIN-2003-08-31 (Finance)
- NEP-FMK-2003-08-31 (Financial Markets)
- NEP-RMG-2003-08-31 (Risk Management)
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