Hedge Portfolios in Markets with Price Discontinuities

University of Technology Sydney Research Paper No. 218

28 Pages Posted: 12 May 2008

See all articles by Gerald H. L. Cheang

Gerald H. L. Cheang

Nanyang Technological University - Business School

Carl Chiarella

University of Technology, Sydney - UTS Business School, Finance Discipline Group

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

Cheang, Gerald Hock Lye and Chiarella, Carl, Hedge Portfolios in Markets with Price Discontinuities (April 1, 2008). University of Technology Sydney Research Paper No. 218, Available at SSRN: https://ssrn.com/abstract=1129063 or http://dx.doi.org/10.2139/ssrn.1129063

Gerald Hock Lye Cheang

Nanyang Technological University - Business School ( email )

Nanyang Avenue
Singapore 639798
Singapore

Carl Chiarella (Contact Author)

University of Technology, Sydney - UTS Business School, Finance Discipline Group ( email )

PO Box 123
Broadway, NSW 2007
Australia
+61 2 9514 7719 (Phone)
+61 2 9514 7711 (Fax)

HOME PAGE: http://www.business.uts.edu.au/finance/

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