Exchange Options Under Jump-Diffusion Dynamics
AbstractMargrabe 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.
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Bibliographic InfoPaper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 235.
Date of creation: 01 Oct 2008
Date of revision:
American options; exchange options; compound Poisson processes; equivalent martingale measure;
Other versions of this item:
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- 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.
- 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.
- Mark Broadie & Jér�me Detemple, 1997. "The Valuation of American Options on Multiple Assets," Mathematical Finance, Wiley Blackwell, vol. 7(3), pages 241-286.
- 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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