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American Option Pricing Using Simulation and Regression: Numerical Convergence Results

Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 19)

Abstract

Recently, simulation methods combined with regression techniques have gained importance when it comes to American option pricing. In this paper, we consider such methods and we examine numerically their convergence properties. We first consider the Least Squares Monte-Carlo (LSM) method of (Longstaff and Schwartz, Rev. Financ. Stud., 14:113–147, 2001) and report convergence rates for the cross-sectional regressions as well as for the estimated price. The results show that the method converges fast, and this holds even with multiple early exercises and with multiple stochastic factors as long as the payoff function is smooth. We also compare the convergence rates to those obtained when using the related methods proposed by (Carriere, Insur. Math. Econ., 19:19–30, 1996; Tsitsiklis JN, Van Roy, IEEE Trans. Neural Network, 12(4):694–703, 2001). The results show that the price estimates from the latter methods converge significantly slower in the multi-period situation.

Keywords

Convergence Rate Option Price Conditional Expectation Exercise Time Early Exercise 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of FinanceHEC MontrealMontrealCanada

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