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Pricing American options written on two underlying assets

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  • Carl Chiarella
  • Jonathan Ziveyi

Abstract

This paper extends the integral transform approach of McKean [ Ind. Manage. Rev. , 1965, 6 , 32--39] and Chiarella and Ziogas [ J. Econ. Dyn. Control , 2005, 29 , 229--263] to the pricing of American options written on more than one underlying asset under the Black and Scholes [ J. Polit. Econ. , 1973, 81 , 637--659] framework. A bivariate transition density function of the two underlying stochastic processes is derived by solving the associated backward Kolmogorov partial differential equation. Fourier transform techniques are used to transform the partial differential equation to a corresponding ordinary differential equation whose solution can be readily found by using the integrating factor method. An integral expression of the American option written on any two assets is then obtained by applying Duhamel's principle. A numerical algorithm for calculating American spread call option prices is given as an example, with the corresponding early exercise boundaries approximated by linear functions. Numerical results are presented and comparisons made with other alternative approaches.

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  • Carl Chiarella & Jonathan Ziveyi, 2014. "Pricing American options written on two underlying assets," Quantitative Finance, Taylor & Francis Journals, vol. 14(3), pages 409-426, March.
    • Handle: RePEc:taf:quantf:v:14:y:2014:i:3:p:409-426
    DOI: 10.1080/14697688.2013.810811
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    2. Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2021. "A Numerical Approach to Pricing Exchange Options under Stochastic Volatility and Jump-Diffusion Dynamics," Papers 2106.07362, arXiv.org.
    3. Len Patrick Dominic M. Garces & Gerald H. L. Cheang, 2020. "A Put-Call Transformation of the Exchange Option Problem under Stochastic Volatility and Jump Diffusion Dynamics," Papers 2002.10194, arXiv.org.
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    5. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.

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