Pricing American options: A duality approach

Operations Research

Volumn 52, Issue 2, 2004, Pages 258-270

  Haugh, Martin B ^a   Kogan, Leonid ^b  

^a Columbia University ^*  (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Duality; Dynamic programming: Approximate dynamic programming; Finance: Asset pricing: American options; Monte Carlo simulation; Optimal stopping

Indexed keywords

AMERICAN OPTIONS; APPROXIMATE DYNAMIC PROGRAMMING; ASSET PRICING; DUALITY; OPTIMAL STOPPING;

APPROXIMATION THEORY; COMPUTER SIMULATION; DYNAMIC PROGRAMMING; FINANCE; MONTE CARLO METHODS; PROBLEM SOLVING; RANDOM PROCESSES;

OPERATIONS RESEARCH;

EID: 1842451051     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.1030.0070     Document Type: Article

References (38)

1. Andersen, L., M. Broadie. 2001. A primal-dual simulation algorithm for pricing multi-dimensional American options. Working paper, Columbia University, New York.
2. Barraquand, J., D. Martineau. 1995. Numerical valuation of high-dimensional multivariate American securities. J. Financial Quant. Anal. 30 383-405.
3. Bensoussan, A. 1984. On the theory of option pricing. Acta Applicandae Mathematicae 2 139-158.
4. Bertsekas, D., J. Tsitsiklis. 1996. Neuro-Dynamic Programming. Athena Scientific, Belmont, MA.
5. Billingsley, P. 1995. Probability and Measure, 3rd ed. John Wiley and Sons, New York.
6. Birge, J. R. 1994. Quasi-Monte Carlo approaches to option pricing. Technical report 94-19, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI.
7. Bossaerts, P. 1989. Simulation estimators of optimal early exercise. Working paper, Carnegie Mellon University, Pittsburgh, PA.
8. Boyle, P., M. Broadie, P. Glasserman. 1997. Monte Carlo methods for security pricing. J. Econom. Dynam. Control 21 1267-1321.
9. Boyle, P., A. W. Kolkiewicz, K. S. Tan. 2001. Pricing American style options using low discrepancy mesh methods. Working paper, University of Waterloo, Waterloo, Ontario, Canada.
10. Broadie, M., P. Glasserman. 1997a. Pricing American-style securities using simulation. J. Econom. Dynam. Control 21 1323-1352.
11. Broadie, M., P. Glasserman. 1997b. A stochastic mesh method for pricing high-dimensional American options. Working paper, Columbia Business School, Columbia University, New York.
12. Broadie, M., P. Glasserman, G. Jain. 1997. Enhanced Monte Carlo estimates for American option prices. J. Derivatives 5 25-44.
13. Carriere, J. 1996. Valuation of early-exercise price of options using simulations and nonparametric regression. Insurance: Math. Econom. 19 19-30.
14. Duffie, Darrell. 1996. Dynamic Asset Pricing Theory. Princeton University Press, Princeton, NJ.
15. Garcia, D. 1999. A Monte Carlo method for pricing American options. Working paper, University of California at Berkeley, CA.
16. Garcia, R., J. Detemple, M. Rindisbacher. 2003. A Monte-Carlo method for optimal portfolios. J. Finance 58 401-446.
17. Geske, R., H. E. Johnson. 1984. The American put options valued analytically. J. Finance 39 1511-1524.
18. Goonatilake, S., P. Treleaven, eds. 1995. Intelligent Systems for Finance and Business. John Wiley and Sons, New York.
19. Harrison, J. M., D. Kreps. 1979. Martingales and arbitrage in multiperiod securities markets. J. Econom. Theory 20 381-408.
20. Harrison, J. M., S. R. Pliska. 1981. Martingales and stochastic integrals in the theory of continuous trading. Stochastic Processes Their Appl. 11 215-260.
21. Hornick, K., M. Stinchcombe, H. White. 1989. Multilayer feedforward networks are universal approximators. Neural Networks 2 359-366.
22. Hutchinson, A., A. Lo, T. Poggio. 1994. A nonparametric approach to the pricing and hedging of derivative securities via learning networks. J. finance 49 851-889.
23. Ibanez, A., F. Zapatero. 2002. Monte Carlo valuation of American options through computation of the optimal exercise frontier. Instituto Tecnologico Autonomo de Mexico.
24. Joy, C., P. P. Boyle, K. S. Tan. 1996. Quasi-Monte Carlo methods in numerical finance. Management Sci. 42 926-938.
25. Karatzas, I. 1998. On the pricing of American options. Appl. Math. Optim. 17 37-60.
26. Karatzas, I., Shreve. 1998. Methods of Mathematical Finance. Springer-Verlag, New York.
27. Longstaff, F., E. Schwartz. 2001. Valuing American options by simulation: a simple least-squares approach. Rev. Financial Stud. 14 113-148.
28. Niederreiter, H. 1992. Random number generation and quasi-Monte Carlo methods. CBMS-NSF 63, SIAM, Philadelphia, PA.
29. Paskov, S., J. Traub. 1995. Faster valuation of financial derivatives. J. Portfolio Management 22(Fall) 113-120.
30. Pliska, S. 1997. Introduction to Mathematical Finance. Blackwell Publishers, Inc., Maiden, MA.
31. Press, W. H., S. A. Teukolsky, S. A. Vetterling, W. T. Flannery. 1992. Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. Cambridge University Press, Cambridge, U.K.
32. Raymar, S., M. Zwecher. 1997. A Monte Carlo valuation of American call options on the maximum of several stocks. J. Derivatives 5 7-23.
33. Rogers, L. C. G. 2002. Monte Carlo valuation of American options. Math. Finance 12 271-286.
34. Tezuka, S. 1995. Uniform Random Numbers: Theory and Practice. Kluwer Academic Publishers, Boston, MA.
35. Tilley, J. A. 1993. Valuing American options in a path simulation model. Trans. Soc. Actuaries 45 83-104.
36. Tsitsiklis, J., B. Van Roy. 1999. Optimal stopping of Markov processes: Hilbert space theory, approximation algorithms, and an application to pricing financial derivatives. IEEE Trans. Auto. Control 44 1840-1851.
37. Tsitsiklis, J., B. Van Roy. 2001. Regression methods for pricing complex American-style options. IEEE Trans. Neural Networks 12 694-703.
38. Vapnik, V. N. 1999. The Nature of Statistical Learning Theory (Statistics for Engineering and Information Science), 2nd ed. Springer Verlag, New York.