On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives
This paper analyses the robustness of Least-Squares Monte Carlo, a technique proposed by Longstaff and Schwartz (2001) for pricing American options. This method is based on least-squares regressions in which the explanatory variables are certain polynomial functions. We analyze the impact of different basis functions on option prices. Numerical results for American put options show that this approach is quite robust to the choice of basis functions. For more complex derivatives, this choice can slightly affect option prices.
Unable to display preview. Download preview PDF.
- Abramowitz, W. and I. Stegun. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover Publications.Google Scholar
- Ait-Sahlia, F. (1996). “Optimal Stopping and Weak Convergence Methods for Some Problems in Financial Economics,” Ph.D. Dissertation, Department of Operations Research, Stanford University.Google Scholar
- Ait-Sahlia, F. and P. Carr. (1997). “American Options: A Comparison of Numerical Methods.” In L.C.G. Rogers and D. Talay (eds.), Numerical Methods in Finance. Cambridge University Press.Google Scholar
- Ait-Sahlia, F. and T.L. Lai. (1996). “Approximations for American Options,” Working Paper, Cornell University.Google Scholar
- Ait-Sahlia, F. and T.L. Lai. (2000). “A Canonical Optimal Stopping Problem for American Options and its Numerical Solution,” Journal of Computational Finance 3, 2, 33¶52.Google Scholar
- Bossaerts, P. (1989). “Simulation Estimators of Optimal Early Exercise,” Working Paper, Carnegie-Mellon University.Google Scholar
- Broadie, M. and P. Glasserman. (1997b). “A Stochastic Mesh Method for Pricing High-Dimensional American Options,” Working Paper, Columbia University.Google Scholar
- Broadie, M., P. Glasserman, and G. Jain. (1997). “Enhanced Monte Carlo Estimation for American Option Prices,” Journal of Derivatives 5, 1, 25¶44.Google Scholar
- Carr, P., R. Jarrow, and R. Mynemi. (1992). “Alternative Characterization of American Puts,” Mathematical Finance 2, 87¶106.Google Scholar
- Demidowitsch, B.P., I.A. Maron, and E.S. Schuwalowa. (1980). Métodos Numéricos de Análisis. Madrid: Editorial Paraninfo.Google Scholar
- Jacka, S.D. (1991). “Optimal Stopping and the American Put,” Mathematical Finance 1, 1¶14.Google Scholar
- McKean, H.P. (1965). “Appendix: A Free Boundary Problem for the Heat Equation Arising from a Problem in Mathematical Economics,” Industrial Management Review 6, 32¶39.Google Scholar
- Raymar, S. and M. Zwecher. (1997). “Monte Carlo Estimation of American Call Options on the Maximum of Several Stocks,” Journal of Derivatives 5, 7¶24.Google Scholar