On the robustness of Least-Squares Monte Carlo (LSM) for pricing American derivatives

Review of Derivatives Research

Volumn 6, Issue 2, 2003, Pages 107-128

  Moreno, Manuel ^a   Navas, Javier F ^b  

^a DEPARTMENT OF ECONOMICS AND BUSINESS   (Spain)

^b IE BUSINESS SCHOOL   (Spain)

Author keywords

American options; Least Squares Monte Carlo; Option pricing

Indexed keywords

EID: 3943051339     PISSN: 13806645     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1027340210935     Document Type: Article

References (45)

1. Abramowitz, W. and I. Stegun. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover Publications.
2. 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.
3. 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.
4. Ait-Sahlia, F. and T.L. Lai. (1996). "Approximations for American Options," Working Paper, Cornell University.
5. 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.
6. Barone-Adesi, G. and R.E. Whaley. (1987). "Efficient Analytic Approximation of American Option Values," Journal of Finance 42, 2, 301-320.
7. Barraquand, J. and D. Martineau. (1995). "Numerical Valuation of High-Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis 30, 383-405.
8. Black, F. and M. Scholes. (1973). "The Pricing of Options and Corporate Liabilities," Journal of Political Economy 81, 3, 637-654.
9. Bossaerts, P. (1989). "Simulation Estimators of Optimal Early Exercise," Working Paper, Carnegie-Mellon University.
10. Boyle, P. (1977). "Options: A Monte Carlo Approach," Journal of Financial Economics 4, 323-338.
11. Boyle, P., M. Broadie, and P. Glasserman. (1997). "Monte Carlo Methods for Security Pricing," Journal of Economic Dynamics and Control 21, 1267-1321.
12. Brennan, M.J. and E.S. Schwartz. (1977). "The Valuation of American Put Options," Journal of Finance 32, 449-462.
13. Brennan, M.J. and E.S. Schwartz. (1978). "Finite Difference Methods and Jump Processes Arising in the Pricing of Contingent Claims: A Synthesis," Journal of Financial and Quantitative Analysis 13, 461-474.
14. Broadie, M. and J. Detemple. (1996). "American Option Valuation: New Bounds, Approximations and a Comparison of Existing Methods," Review of Financial Studies 9, 1211-1250.
15. Broadie, M. and P. Glasserman. (1997a). "Pricing American-Style Securities using Simulations," Journal of Economic Dynamics and Control 21, 1323-1352.
16. Broadie, M. and P. Glasserman. (1997b). "A Stochastic Mesh Method for Pricing High-Dimensional American Options," Working Paper, Columbia University.
17. Broadie, M., P. Glasserman, and G. Jain. (1997). "Enhanced Monte Carlo Estimation for American Option Prices," Journal of Derivatives 5, 1, 25-44.
18. Bunch, D. and H.E. Johnson. (1992). "A Simple and Numerically Efficient Valuation Method for American Puts Using a Modified Geske-Johnson Approach," Journal of Finance 47, 2, 809-816.
19. Bunch, D. and H.E. Johnson. (2000). "The American Put Option and Its Critical Stock Price," Journal of Finance 55, 5, 2333-2356.
20. Carr, P. (1998). "Randomization and the American Put," Review of Financial Studies 11, 597-626.
21. Carr, P., R. Jarrow, and R. Mynemi. (1992). "Alternative Characterization of American Puts," Mathematical Finance 2, 87-106.
22. Carriere, J.F. (1996). "Valuation of the Early-Exercise Price for Options Using Simulations and Nonparametric Regresion," Insurance, Mathematics and Economics 19, 19-30.
23. Clément, E., D. Lamberton, and P. Protter. (2002). "An Analysis of a Least Squares Regression Method for American Option Pricing," Finance and Stochastics 6, 4, 449-471.
24. Courtadon, G. (1982). "A More Accurate Finite Difference Approximation for the Valuation of Options," Journal of Financial and Quantitative Analysis 17, 5, 697-703.
25. Cox, J.C., S.A. Ross, and M. Rubinstein. (1979). "Option Pricing: A Simplified Approach," Journal of Financial Economics 7, 3, 229-263.
26. Demidowitsch, B.P., I.A. Maron, and E.S. Schuwalowa. (1980). Métodos Numéricos de Análisis. Madrid: Editorial Paraninfo.
27. Geske, R. (1979). "A Note on an Analytical Valuation Formula for Unprotected American Options on Stocks with Known Dividends," Journal of Financial Economics 7, 375-380.
28. Geske, R. and H.E. Johnson. (1984). "The American Put Option Valued Analytically," Journal of Finance 39, 5, 1511-1524.
29. Ho, T.S.Y., R.C. Stapleton, and M.G. Subrahmanyam. (1997). "The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique," Journal of Finance 52, 2, 827-840.
30. Jacka, S.D. (1991). "Optimal Stopping and the American Put," Mathematical Finance 1, 1-14.
31. Johnson, H.E. (1983). "An Analytic Approximation for the American Put Price," Journal of Financial and Quantitative Analysis 18, 1, 141-148.
32. Ju, N. (1998). "Pricing American Option by Approximating its Early Exercise Boundary as a Multipiece Exponential Function," Review of Financial Studies 11, 3, 627-646.
33. Ju, N. and R. Zhong. (1999). "An Approximate Formula for Pricing American Options," The Journal of Derivatives 7, 2, 31-40.
34. Kim, I.J. (1990). "The Analytical Valuation of American Options," Review of Financial Studies 3, 547-572.
35. Longstaff, F.A. and E.S. Schwartz. (2001). "Valuing American Options by Simulations: A Simple Least-Squares Approach," Review of Financial Studies 14, 1, 113-147.
36. 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.
37. Merton, R.C. (1973). "Theory of Rational Option Pricing," Bell Journal of Economics and Management Science 4, 1, 141-183.
38. Parkinson, M. (1977). "Option Pricing: The American Put," Journal of Business 50, 21-36.
39. 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.
40. Rendleman, R. and B. Bartter. (1979). "Two-State Option Pricing," Journal of Finance 34, 1093-1110.
41. Roll, R. (1977). "An Analytic Valuation Formula for Unprotected American Call Options on Stocks with Known Dividends," Journal of Financial Economics 5, 251-258.
42. Schwartz, E.S. (1977). "The Valuation of Warrants: Implementing a New Approach," Journal of Financial Economics 4, 79-93.
43. Tsitsiklis, J.N. and B. Van Roy. (1999). "Optimal Stopping of Markov Processes: Hilbert Space, Theory, Approximation Algorithms, and an Application to Pricing High-Dimensional Financial Derivatives," IEEE Transactions on Automatic Control 44, 10, 1840-1851.
44. Tsitsiklis, J.N. and B. Van Roy. (2001). "Regression Methods for Pricing Complex American-Style Options," IEEE Transactions on Neural Networks 12, 4, 694-703.
45. Whaley, R.E. (1981). "On the Valuation of American Call Options on Stocks with Known Dividends," Journal of Financial Economics 9, 2, 207-211.