Exchange Options Under Jump-Diffusion Dynamics

Gerald H. L. Cheang and Carl Chiarella ()
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Gerald H. L. Cheang: Division of Banking and Finance, Nanyang Business School, Nanyang Technological University

No 235, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: Margrabe provides a pricing formula for an exchange option where the distributions of both stock prices are log-normal with correlated Wiener components. Merton has provided a formula for the price of a European call option on a single stock where the stock price process contains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. We use Merton?s analysis to extend Margrabe?s results to the case of exchange options where both stock price processes also contain compound Poisson jump components. A Radon-Nikod´ym derivative process that induces the change of measure from the market measure to an equivalent martingale measure is introduced. The choice of parameters in the Radon-Nikod´ym derivative allows us to price the option under different financial-economic scenarios. We also consider American style exchange options and provide a probabilistic intepretation of the early exercise premium.

Keywords: American options; exchange options; compound Poisson processes; equivalent martingale measure (search for similar items in EconPapers)
JEL-codes: G12 G13 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-bec
Date: 2008-10-01
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