Hedge Portfolios in Markets with Price Discontinuities

Gerald H.L. Cheang and Carl Chiarella

No 218, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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 (search for similar items in EconPapers)
JEL-codes: C00 G12 G13 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2008-03-01
New Economics Papers: this item is included in nep-bec and nep-fmk
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