A Quasi-Analytical Interpolation Method for Pricing American Options Under General Multi-Dimensional Diffusion Processes

Posted: 9 Jun 2010

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Date Written: June 8, 2010

Abstract

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson in J Financ Quant Anal 18(1):141–148 (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 efficiency as the quadratic approximation of Barone-Adesi and Whaley in J Financ 42:301–320 (1987), 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 efficient and fairly accurate.

Keywords: American option, Interpolation method, Quasi-analytical approximation, Critical boundary, Heston’s Stochastic volatility model

JEL Classification: C02, C63, G13

Suggested Citation

Li, Minqiang, A Quasi-Analytical Interpolation Method for Pricing American Options Under General Multi-Dimensional Diffusion Processes (June 8, 2010). Review of Derivatives Research, Vol. 13, No. 2, pp. 177-217, 2010, Available at SSRN: https://ssrn.com/abstract=1622367

Minqiang Li (Contact Author)

Bloomberg LP ( email )

731 Lexington Avenue
New York, NY 10022
United States

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