Approximating free exercise boundaries for American-style options using simulation and optimization

Monte Carlo simulation can be readily applied to asset pricing problems with multiple state variables and possible path dependencies because convergence of Monte Carlo methods is independent of the number of state variables. This paper applies Monte Carlo simulation to the problem of determining free exercise boundaries for pricing American-style options. We use a simulation-optimization method to identify approximately optimal exercise thresholds that are defined by a minimal number of parameters. We demonstrate that asset prices calculated using this method are comparable to those found using other numerical asset pricing methods.

[1]  Michael C. Fu.  Pricing of financial derivatives via simulation , 1995, WSC '95.

[2]  John M. Charnes,et al.  Using simulation for option pricing , 2000, 2000 Winter Simulation Conference Proceedings (Cat. No.00CH37165).

[3]  James A. Tilley.  Valuing American Options in a Path Simulation Model , 2002 .

[4]  M. Fu,et al.  Pricing American Options: A Comparison of Monte Carlo Simulation Approaches ⁄ , 2001 .

[5]  Fred W. Glover,et al.  New advances and applications of combining simulation and optimization , 1996, WSC.

[6]  Paul Glasserman,et al.  Monte Carlo Methods in Financial Engineering , 2003 .

[7]  Dwight Grant,et al.  Path-dependent options: extending the Monte Carlo simulation approach , 1997 .

[8]  John M. Charnes,et al.  Options pricing: using simulation for option pricing , 2000, WSC '00.

[9]  Steven Raymar,et al.  Monte Carlo Estimation of American Call Options on the Maximum of Several Stocks , 1997 .

[10]  Michael C. Fu,et al.  Sensitivity Analysis for Monte Carlo Simulation of Option Pricing , 1995, Probability in the Engineering and Informational Sciences.

[11]  Francis A. Longstaff,et al.  Valuing American Options by Simulation: A Simple Least-Squares Approach , 2001 .

[12]  Dawn Hunter,et al.  A stochastic mesh method for pricing high-dimensional American options , 2004 .

[13]  Michael C. Fu,et al.  Optimal Exercise Policies and Simulation-Based Valuation for American-Asian Options , 2003, Oper. Res..

[14]  P. Boyle.  Options: A Monte Carlo approach , 1977 .

[15]  J. Carriére.  Valuation of the early-exercise price for options using simulations and nonparametric regression , 1996 .

[16]  Jérôme Barraquand,et al.  Numerical Valuation of High Dimensional Multivariate American Securities , 1995, Journal of Financial and Quantitative Analysis.

[17]  Fernando Zapatero,et al.  Monte Carlo Valuation of American Options through Computation of the Optimal Exercise Frontier , 2000, Journal of Financial and Quantitative Analysis.

[18]  P. Glasserman,et al.  A Sotchastic Mesh Method for Pricing High-Dimensional American Options , 2004 .

[19]  P. Glasserman,et al.  Pricing American-style securities using simulation , 1997 .

[20]  M. Fu,et al.  Pricing of financial derivatives via simulation , 1995, Winter Simulation Conference Proceedings, 1995..