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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.

Suggested Citation

  • 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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    References listed on IDEAS

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    1. Carl Chiarella & Boda Kang & Gunter H. Meyer & Andrew Ziogas, 2009. "The Evaluation Of American Option Prices Under Stochastic Volatility And Jump-Diffusion Dynamics Using The Method Of Lines," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 393-425.
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    4. Huang, Jing-zhi & Subrahmanyam, Marti G & Yu, G George, 1996. "Pricing and Hedging American Options: A Recursive Integration Method," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 277-300.
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    6. Elias Tzavalis & Shijun Wang, 2003. "Pricing American Options under Stochastic Volatility: A New Method Using Chebyshev Polynomials to Approximate the Early Exercise Boundary," Working Papers 488, Queen Mary University of London, School of Economics and Finance.
    7. Geltner, David & Riddiough, Timothy & Stojanovic, Srdjan, 1996. "Insights on the Effect of Land Use Choice: The Perpetual Option on the Best of Two Underlying Assets," Journal of Urban Economics, Elsevier, vol. 39(1), pages 20-50, January.
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    Cited by:

    1. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
    2. Shen, Yang & Sherris, Michael & Ziveyi, Jonathan, 2016. "Valuation of guaranteed minimum maturity benefits in variable annuities with surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 127-137.

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