FX risk-neutral valuation relationships for the SU jump-diffusion family

Abstract

This paper derives preference-free pricing formulae for foreign exchange options, which are consistent with a general equilibrium representative agent economy. These risk-neutral valuation relationships (RNVR's) are obtained for the S_U jump-diffusion family. Call and put options are particular cases of our general model. These option pricing formulae nest Merton's (1976) jump-diffusion equations. Our option valuation formulae are able to generate symmetric and asymmetric volatility smiles and skews with similar shapes to those observed in the foreign exchange options market, and they solve several pricing biases of Black (1976) and Garman and Kohlhagen (1983) models. Copyright © 2010 John Wiley & Sons, Ltd.