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A Quasi-analytical Interpolation Method for Pricing American Options under General Multi-dimensional Diffusion Processes

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Li, Minqiang

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Abstract

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical regression. The method can be adapted to general diffusion processes as long as quick and accurate pricing methods exist for the corresponding European and perpetual American options. The American option price is shown to be approximately equal to an interpolation of two European option prices with the interpolation weight proportional to a perpetual American option. In the Black-Scholes model, our method achieves the same e±ciency as Barone-Adesi and Whaley's (1987) quadratic approximation with our method being generally more accurate for out-of-the-money and long-maturity options. When applied to Heston's stochastic volatility model, our method is shown to be extremely e±cient and fairly accurate.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 17348.

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Date of creation: 2009
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Handle: RePEc:pra:mprapa:17348

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Related research
Keywords: American option; Interpolation method; Quasi-analytical approximation; Critical bound- ary; Heston's Stochastic volatility model;

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Find related papers by JEL classification:
C63 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Computational Techniques
C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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  1. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March. [Downloadable!] (restricted)
  2. Parkinson, Michael, 1977. "Option Pricing: The American Put," Journal of Business, University of Chicago Press, vol. 50(1), pages 21-36, January. [Downloadable!] (restricted)
  3. Huang, Jing-zhi & Subrahmanyam, Marti G & Yu, G George, 1996. "Pricing and Hedging American Options: A Recursive Integration Method," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 277-300. [Downloadable!] (restricted)
  4. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. " General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December. [Downloadable!] (restricted)
  5. Johnson, H. E., 1983. "An Analytic Approximation for the American Put Price," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(01), pages 141-148, March. [Downloadable!]
  6. Manuel Moreno & Javier Navas, 2003. "On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives," Review of Derivatives Research, Springer, vol. 6(2), pages 107-128, May. [Downloadable!] (restricted)
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  7. Song-Ping Zhu, 2006. "An exact and explicit solution for the valuation of American put options," Quantitative Finance, Taylor and Francis Journals, vol. 6(3), pages 229-242, June. [Downloadable!] (restricted)
  8. Brennan, Michael J & Schwartz, Eduardo S, 1977. "The Valuation of American Put Options," Journal of Finance, American Finance Association, vol. 32(2), pages 449-62, May. [Downloadable!] (restricted)
  9. Barone-Adesi, Giovanni, 2005. "The saga of the American put," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2909-2918, November. [Downloadable!] (restricted)
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  12. Broadie, Mark & Glasserman, Paul, 1997. "Pricing American-style securities using simulation," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1323-1352, June. [Downloadable!] (restricted)
  13. Sullivan, Michael A, 2000. "Valuing American Put Options Using Gaussian Quadrature," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(1), pages 75-94.
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  15. Geske, Robert & Johnson, Herb E, 1984. " The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-24, December. [Downloadable!] (restricted)
  16. Song-Ping Zhu & Zhi-Wei He, 2007. "Calculating The Early Exercise Boundary Of American Put Options With An Approximation Formula," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(07), pages 1203-1227. [Downloadable!] (restricted)
  17. Zhylyevskyy, Oleksandr (Alex), 2009. "A fast Fourier transform technique for pricing American options under stochastic volatility," Staff General Research Papers 13112, Iowa State University, Department of Economics.
  18. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
  19. David S. Bunch & Herb Johnson, 2000. "The American Put Option and Its Critical Stock Price," Journal of Finance, American Finance Association, vol. 55(5), pages 2333-2356, October. [Downloadable!] (restricted)
  20. Minqiang Li, Li, 2009. "Analytical Approximations for the Critical Stock Prices of American Options: A Performance Comparison," MPRA Paper 15018, University Library of Munich, Germany. [Downloadable!]
  21. Breen, Richard, 1991. "The Accelerated Binomial Option Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(02), pages 153-164, June. [Downloadable!]
  22. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, . "General Properties of Option Prices (Revision of 11-95) (Reprint 058)," Rodney L. White Center for Financial Research Working Papers 1-96, Wharton School Rodney L. White Center for Financial Research.
    Other versions:
  23. Carr, Peter, 1998. "Randomization and the American Put," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 11(3), pages 597-626.
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