A survey of simulation-based methods for pricing complex American type options

This paper gives an overview of simulation-based methods which have been developed for the valuation of “complex” American type options that cannot be valued analytically. The authors focus on one especially promising approach which we call “bounded recursive stochastic simulation” (BRSS) after having stripped off some time consuming but dispensable working steps. Then, we test the BRSS-approach by comparing it with three other simulation-based methods. Because of its superiority with regard to accuracy, computational costs, and flexibility, the paper describes the BRSS-approach in detail, thus, providing scientific know-how for efficient numerical option pricing.

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

[2]  Richard H. Bernhard,et al.  INVESTMENT UNDER UNCERTAINTY Princeton University Press, Princeton, New Jersey, 1994, xiv + 468 pp. ISBN 0-69I-034I0-9. List: S39.50. , 1995 .

[3]  Alfredo Ibáñez,et al.  Valuation by Simulation of Contingent Claims with Multiple Early Exercise Opportunities , 2004 .

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

[5]  D. Rubinfeld,et al.  Econometric models and economic forecasts , 2002 .

[6]  Diderik Lund With Timing Options and Heterogeneous Costs, the Lognormal Diffusion is Hardly an Equilibrium Price Process for Exhaustible Resources , 1992 .

[7]  A. Balmann,et al.  Real Options and Competition: The Impact of Depreciation and Reinvestment , 2002 .

[8]  Sarah Rothstein Options Futures And Other Derivative Securities , 2016 .

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

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

[11]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[12]  E. Haug The complete guide to option pricing formulas , 1997 .

[13]  Philip Protter,et al.  An analysis of a least squares regression method for American option pricing , 2002, Finance Stochastics.

[14]  Wayne L. Winston Financial Models Using Simulation and Optimization , 1998 .

[15]  Mondher Bellalah,et al.  Options, Futures and Exotic Derivatives: Theory, Application and Practice , 1998 .

[16]  S. Ross,et al.  Option pricing: A simplified approach☆ , 1979 .

[17]  S. Ross,et al.  The valuation of options for alternative stochastic processes , 1976 .

[18]  Manuel Moreno,et al.  On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives , 2007 .

[19]  R. C. Merton,et al.  Theory of Rational Option Pricing , 2015, World Scientific Reference on Contingent Claims Analysis in Corporate Finance.

[20]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[21]  William J. Morokoff Generating Quasi-Random Paths for Stochastic Processes , 1998, SIAM Rev..

[22]  Dwight Grant,et al.  Simulation and the Early Exercise Option Problem , 1997 .

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

[24]  Dawn Hunter Pricing American options: a comparison of Monte Carlo simulation approaches , 2001 .

[25]  M. Fu,et al.  Optimization of discrete event systems via simultaneous perturbation stochastic approximation , 1997 .

[26]  John N. Tsitsiklis,et al.  Regression methods for pricing complex American-style options , 2001, IEEE Trans. Neural Networks.

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

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

[29]  M. A. Dias Selection of Alternatives of Investment in Information for Oilfield Development Using Evolutionary Real Options Approach Version Date : April 28 , 2001 By : , 2001 .

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

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

[32]  P. Glasserman,et al.  Estimating security price derivatives using simulation , 1996 .

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