Exchange Options Under Jump-Diffusion Dynamics

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Journal Article
Applied Mathematical Finance, 2011, 18 (3), pp. 245 - 276
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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 RadonNikody´m derivative process that induces the change of measure from the market measure to an equivalent martingale measure. The choice of parameters in the RadonNikody´m 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.
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