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American option pricing under stochastic volatility: an efficient numerical approach. (English) Zbl 1186.91203

Summary: This paper develops a new numerical technique to price an American option written upon an underlying asset that follows a bivariate diffusion process. The technique presented here exploits the supermartingale representation of an American option price together with a coarse approximation of its early exercise surface that is based on an efficient implementation of the least-squares Monte-Carlo algorithm (LSM) of F. A. Longstaff and E. S. Schwartz [“Valuing American options by simulation: a simple least-squares approach”, Rev. Financ. Stud. 14, 113–147 (2001)]. Our approach also has the advantage of avoiding two main issues associated with LSM, namely its inherent bias and the basis functions selection problem. Extensive numerical results show that our approach yields very accurate prices in a computationally efficient manner. Finally, the flexibility of our method allows for its extension to a much larger class of optimal stopping problems than addressed in this paper.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
65C05 Monte Carlo methods
90C59 Approximation methods and heuristics in mathematical programming
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