Pricing American Put Options Using Stochastic Optimization Methods

G. Yin (), J. W. Wang (), Q. Zhang (), Y. J. Liu () and R. H. Liu ()
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G. Yin: Wayne State University
J. W. Wang: Moodys Investors Service
Q. Zhang: The University of Georgia
Y. J. Liu: Missouri Southern State University
R. H. Liu: University of Dayton

Chapter Chapter 15 in Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, 2006, pp 301-329 from Springer

Abstract: Abstract This work develops a class of stochastic optimization algorithms for pricing American put options. The stock model is a regime-switching geometric Brownian motion. The switching process represents macro market states such as market trends, interest rates, etc. The solutions of pricing American options may be characterized by certain threshold values. Here, we show how one can use a stochastic approximation (SA) method to determine the optimal threshold levels. For option pricing in a finite horizon, a SA procedure is carried for a fixed time T. As T varies, the optimal threshold values obtained using stochastic approximation trace out a curve, called the threshold frontier. Convergence and rates of convergence are obtained using weak convergence methods and martingale averaging techniques. The proposed approach provides us with a viable computational approach, and has advantage in terms of the reduced computational complexity compared with the variational or quasi-variational inequality approach for optimal stopping.

Keywords: Stochastic approximation; stochastic optimization; weak convergence; geometric Brownian motion; regime switching; American put option (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:isochp:978-0-387-33815-6_15

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DOI: 10.1007/0-387-33815-2_15

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