Asymptotically optimal importance sampling and stratification for pricing path-dependent options

Mathematical Finance

Volumn 9, Issue 2, 1999, Pages 117-152

  Glasserman, Paul ^a   Heidelberger, Philip ^b   Shahabuddin, Perwez ^b  

^a Columbia University ^*  (United States)

^b NONE

Author keywords

Laplace principle; Large deviations; Monte Carlo methods; Variance reduction

Indexed keywords

EID: 0033411026     PISSN: 09601627     EISSN: None     Source Type: Journal    
DOI: 10.1111/1467-9965.00065     Document Type: Article

References (32)

1. ANDERSEN, L. (1995): Efficient Techniques for Simulation of Interest Rate Models Involving Non-Linear Stochastic Differential Equations, working paper, General Re Financial Products, New York, NY.
2. BLEISTEIN, N., and R. A. HANDELSMAN (1975): Asymptotic Expansions of Integrals. New York: Holt, Rinehart, and Winston.
3. BOYLE, P., M. BROADIE, and P. GLASSERMAN (1997): Simulation Methods for Security Pricing, J. Econ. Dynam. Control, 21, 1267-1321.
4. BUCK, R. C. (1978): Advanced Calculus, 3rd ed. New York: McGraw-Hill.
5. CHEN, J.-C, D. Lu, J. S. SADOWSKY, and K. YAO (1993): On Importance Sampling in Digital Communications - Part I: Fundamentals, IEEE J. Selected Areas Commun. 11, 289-299.
6. Cox, J., J. E. INGERSOLL, and S. A. Ross (1985): A Theory of the Term Structure of Interest Rates, Econometrica 53, 385-407.
7. DEMBO, A., and O. ZEITOUNI (1993): Large Deviations Techniques and Applications. Boston: Jones and Bartlett.
8. DEUSCHEL, J. D., and D. STROOCK (1989): Large Deviations. San Diego: Academic Press.
9. DUPUIS, P., and R. ELLIS (1997): A Weak Convergence Approach to the Theory of Large Deviations. New York: Wiley.
10. FOURNIÉ, E., J. M. LASRY, and N. TOUZI (1999): Monte Carlo Methods for Stochastic Volatility Models; in Numerical Methods in Finance, L. C. G. Rogers and D. Talay, eds. New York: Cambridge University Press, 146-164.
11. GEMAN, H., and M. YOR (1993): Bessel Processes, Asian Options, and Perpetuities, Math. Finance 3, 349-375.
12. GLASSERMAN, P., P. HEIDELBERGER, and P. SHAHABUDDIN (1998): Gaussian Importance Sampling and Stratification: Computational Issues, Proceedings of the 1998 Winter Simulation Conference. New York: IEEE Press, 685-693.
13. GLASSERMAN, P., and Y. WANG (1997): Counterexamples in Importance Sampling for Rare Event Probabilities, Annals Appl. Probab. 7, 731-746.
14. HAMMERSLEY, J., and D. HANDSCOMB (1964): Monte Carlo Methods. London: Methuen & Co. Ltd.
15. HEIDELBERGER, P. (1995): Fast Simulation of Rare Events in Queueing and Reliability Models, ACM Trans. Modeling and Computer Simulation 5(1), 43-85.
16. HULL, J., and A. WHITE (1987): The Pricing of Options on Assets with Stochastic Volatilities, J. Finance 42, 281-300.
17. JOHNSON, R. A., and D. W. WICHERN (1982): Applied Multivariate Statistical Analysis. Englewood Cliffs, NJ: Prentice-Hall.
18. KARLIN, S., and H. TAYLOR (1975): A First Course in Stochastic Processes, 2nd ed. New York: Academic Press.
19. KLOEDEN, P., and E. PLATEN (1992): Numerical Solution of Stochastic Differential Equations, Berlin: Springer-Verlag.
20. MARSAGLIA, G., A. ZAMAN, and J. MARSAGLIA (1994): Rapid Evaluation of the Inverse of the Normal Distribution Function, Statistics and Probability Letters 19, 259-266.
21. MARSHALL, A. W., and I. OLKIN (1979): Inequalities: Theory of Majorization and its Applications. New York: Academic Press.
22. McKAY, M. D., W. J. CONOVER, and R. J. BECKMAN (1979): A Comparison of Three Methods for Selecting Input Variables in the Analysis of Output from a Computer Code, Technometrics 21, 239-245.
23. MORO, B. (1995): The Full Monte, RISK 8 (February), 57-58.
24. The Numerical Algorithms Group (1996): NAG C Library Manual, Mark 4. Oxford, UK: NAG, Ltd.
25. NEWTON, N. J. (1994): Variance Reduction for Simulated Diffusions, SIAM J. Appl. Math. 54, 1780-1805.
26. NEWTON, N. J. (1997) Continuous-Time Monte Carlo Methods and Variance Reduction; in Numerical Methods in Finance, L. C. G. Rogers and D. Talay, eds. New York: Cambridge University Press, 22-42.
27. RAO, C. R., and H. TOUTENBURG (1995): Linear Models: Least Squares and Alternatives. New York: Springer-Verlag.
28. REIDER, R. (1993): An Efficient Monte Carlo Technique for Pricing Options, working paper, Wharton School, University of Pennsylvania.
29. ROCKAFELLER, R. T. (1970): Convex Analysis. Princeton, NJ: Princeton University Press.
30. ROGERS, L. C. G. (1995): Which Model for the Term Structure of Interest Rates Should One Use?; in Mathematical Finance, IMA vol. 65, M. H. A. Davis, D. Duffie, and I. Karatzas, eds. New York: Springer, 93-116.
31. SCHOENMAKERS, J, G., and A. W. HEEMINK (1997): Fast Valuation of Financial Derivatives, J. Computat. Finance 1, 47-62.
32. SHAHABUDDIN, P. (1995): Rare Event Simulation in Stochastic Models; in Proceedings of the 1995 Winter Simulation Conference, IEEE Computer Society Press, 178-185.