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A quasi-analytical interpolation method for pricing American options under general multi-dimensional diffusion processes. (English) Zbl 1231.91442

Summary: We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of H. E. Johnson [“An analytic approximation for the American put price”, J. Financ. Quant. Anal. 18, No. 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 G. Barone-Adesi and R. Whaley [“Efficient analytical approximation of American option values”, J. Finance 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.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
65D05 Numerical interpolation
41A05 Interpolation in approximation theory

Software:

Mathematica
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References:

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