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Exchange Options Under Jump-Diffusion Dynamics

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  • Gerald Cheang
  • Carl Chiarella

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.

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File URL: http://www.tandfonline.com/doi/abs/10.1080/1350486X.2010.505390
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 18 (2011)
Issue (Month): 3 ()
Pages: 245-276

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Handle: RePEc:taf:apmtfi:v:18:y:2011:i:3:p:245-276

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Related research

Keywords: American options; exchange options; compound Poisson processes; equivalent martingale measure;

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References

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  1. J. Michael Harrison & Stanley R. Pliska, 1981. "Martingales and Stochastic Integrals in the Theory of Continous Trading," Discussion Papers 454, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  2. David B. Colwell & Robert J. Elliott, 1993. "Discontinuous Asset Prices And Non-Attainable Contingent Claims," Mathematical Finance, Wiley Blackwell, vol. 3(3), pages 295-308.
  3. S. D. Jacka, 1991. "Optimal Stopping and the American Put," Mathematical Finance, Wiley Blackwell, vol. 1(2), pages 1-14.
  4. Chandrasekhar Reddy Gukhal, 2001. "Analytical Valuation of American Options on Jump-Diffusion Processes," Mathematical Finance, Wiley Blackwell, vol. 11(1), pages 97-115.
  5. Mark Broadie & Jér�me Detemple, 1997. "The Valuation of American Options on Multiple Assets," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 241-286.
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Cited by:
  1. Caldana, Ruggero & Fusai, Gianluca, 2013. "A general closed-form spread option pricing formula," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4893-4906.

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