A multinomial approximation for American option prices in Lévy process models

Mathematical Finance

Volumn 16, Issue 4, 2006, Pages 613-633

  Maller, Ross A ^a,c   Solomon, David H ^b   Szimayer, Alex ^a  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b UNIVERSITY OF CHICAGO   (United States)

^c AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

Author keywords

American options; L vy process; Multinomial approximation

Indexed keywords

EID: 33748325708     PISSN: 09601627     EISSN: 14679965     Source Type: Journal    
DOI: 10.1111/j.1467-9965.2006.00286.x     Document Type: Article

References (27)

1. AMIN, K. (1993): Jump Diffusion Option Valuation in Discrete Time, J. Finance 48, 1833-1863.
2. AMIN, K., and A. KHANNA (1994): Convergence of American Option Values from Discrete to Continuous-Time Financial Markets, Math. Finance 4, 289-304.
3. ASMUSSEN, S., and J. ROSINSKI (2001): Approximations of Small Jumps of Levy Processes with a View Towards Simulation, J. Appl. Prob. 38, 482-493.
4. BERTOIN, J. (1996): Lévy Processes. Cambridge: Cambridge University Press.
5. BINGHAM, N. H., and R. KIESEL (2004): Risk-Neutral Valuation, 2nd ed. Berlin: Springer.
6. BLACK, F., and M. SCHOLES (1973): The Pricing of Options and Corporate Liabilities, J. Polit. Econ. 81, 637-654.
7. CHOW, Y. S., and H. TEICHER (1988): Probability Theory: Independence, Interchangeability, Martingales. Heidelberg: Springer.
8. CONT, R., and E. VOLTCHKOVA (2005): Integro-Differential Equations for Option Prices in Exponential Lévy Models, Finance Stochastics 9, 299-325.
9. COX, J. C., S. A. ROSS, and M. RUBINSTEIN (1979): Option Pricing: A Simplified Approach, J. Financial Econ. 3, 125-144.
10. DUFFIE, D. (1988): Security Markets: Stochastic Models. New York: Academic Press.
11. DURRETT, R., and S. RESNICK (1978): Functional Limit Theorems for Dependent Random Variables, Ann. Probab. 6, 829-846.
12. ETHIER, and KURTZ (1986): Markov Processes. New York: Wiley.
13. FU, M. C., S. B. LAPRISE, D. B. MADAN, Y. SU, and R. WU (2001): Pricing American Options: A Comparison of Monte Carlo Simulation Approaches, J. Comput. Finance 2, 62-73.
14. GLASSERMAN, P. (2003): Monte Carlo Methods in Financial Engineering. New York: Springer.
15. HARRISON, M., and S. PLISKA (1981): Martingales and Stochastic Integrals in the Theory of Continuous Trading, Stochastic Processes Appl. 11, 215-260.
16. HIRSA, A., and D. MADAN (2004): Pricing American Options under Variance-Gamma, J. Comput. Finance 1, 63-80.
17. JACOD, J., and A. N. SHIRYAEV (1987): Limit Theorems for Stochastic Processes. Heidelberg: Springer.
18. KËLLEZI, E., and N. WEBBER (2004): Valuing Bermudan Options When Asset Returns Are Lévy Processes, Quant. Finance 4, 87-100.
19. LAMBERTON, D. (1998): Error Estimates for the Binomial Approximation of American Put Options, Ann. Appl. Probab. 8, 206-233.
20. MADAN, D. B., P. P. CARR, and E. C. CHANG (1998): The Variance Gamma Process and Option Pricing, Eur. Finance Rev. 2, 79-105.
21. MATACHE, A.-M., P. A. NITSCHE, and C. SCHWAB (2005): Wavelet Galerkin Pricing of American Options on Lévy Driven Assets, Quant. Finance 5, 403-424.
22. MEYER, P. A., and W. A. ZHENG (1984): Tightness Criteria for Laws of Semimartingales, Ann. Inst. Henri Poincaré 20, 353-372.
23. MULINACCI, S. (1996): An Approximation of American Option Prices in a Jump-Diffusion Model, Stochastic Processes Appl. 62, 1-17.
24. MULINACCI, S., and M. PRATELLI (1998): Functional Convergence of Snell Envelopes: Application to American Options Approximations, Finance Stochastics 2, 311-327.
25. PETROV, V. V. (1975): Sums of Independent Random Variables. Heidelberg: Springer.
26. PROTTER, P. (1990): Stochastic Integration and Differential Equations: A New Approach. New York: Springer.
27. SATO, K. (1999): Lévy Processes and Infinitely Divisible Distributions. Cambridge: Cambridge University Press.