A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes |
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Authors: | Minqiang Li |
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Institution: | 1.College of Management, Georgia Institute of Technology,Atlanta,USA |
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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 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. |
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