Stochastic Optimization Algorithms for Pricing American Put Options Under Regime-Switching Models

This work provides a Markov-modulated stochastic approximation based approach for pricing American put options under a regime-switching geometric Brownian motion market model. The solutions of pricing American options may be characterized by certain threshold values. Here, a class of Markov-modulated stochastic approximation (SA) algorithms is developed to determine the optimal threshold levels. For option pricing in a finite horizon, a SA procedure is carried out for a fixed time T. As T varies, the optimal threshold values obtained via SA trace out a curve, called the threshold frontier. Numerical experiments are reported to demonstrate the effectiveness of the approach. Our approach provides us with a viable computational tool and has advantage in terms of the reduced computational complexity compared with the variational or quasivariational inequality methods for optimal stopping.Communicated by C. T. LeondesThis research was supported in part by the National Science Foundation under Grant DMS-0304928, and in part by the National Natural Science Foundation of China under Grant 60574069.