Hedge Portfolios in Markets with Price Discontinuities
University of Technology Sydney Research Paper No. 218
28 Pages Posted: 12 May 2008
Date Written: April 1, 2008
Abstract
We consider a market consisting of multiple assets under jump-diffusion dynamics with European style options written on these assets. It is well-known that such markets are incomplete in the Harrison and Pliska sense. We derive a pricing relation by adopting a Radon-Nikodym derivative based on the exponential martingale of a correlated Brownian motion process and a multivariate compound Poisson process. The parameters in the Radon-Nikodym derivative define a family of equivalent martingale measures in the model, and we derive the corresponding integro-partial differential equation for the option price. We also derive the pricing relation by setting up a hedge portfolio containing an appropriate number of options to complete the market. The market prices of jump-risks are priced in the hedge portfolio and we relate these to the choice of the parameters in the Radon-Nikodym derivative used in the alternative derivation of the integro-partial differential equation.
Keywords: incomplete markets, equivalent martingale measure, compound Poisson processes, Radon-Nikodym derivative, multi-asset options, integro-partial differential equation
JEL Classification: C00, G12, G13
Suggested Citation: Suggested Citation