Exchange Options Under Jump-Diffusion Dynamics

Gerald Cheang and Carl Chiarella

Applied Mathematical Finance, 2011, vol. 18, issue 3, 245-276

Abstract: This article extends the exchange option model of Margrabe, where the distributions of both stock prices are log-normal with correlated Wiener components, to allow the underlying assets to be driven by jump-diffusion processes of the type originally introduced by Merton. We introduce the Radon-Nikodym derivative process that induces the change of measure from the market measure to an equivalent martingale measure. The choice of parameters in the Radon-Nikodym derivative allows us to price the option under different financial-economic scenarios. We also consider American style exchange options and provide a probabilistic interpretation of the early exercise premium.

Keywords: American options; exchange options; compound Poisson processes; equivalent martingale measure (search for similar items in EconPapers)
Date: 2011
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Working Paper: Exchange Options Under Jump-Diffusion Dynamics (2008)
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DOI: 10.1080/1350486X.2010.505390

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