Error estimates for the binomial approximation of American put options

Annals of Applied Probability

Volumn 8, Issue 1, 1998, Pages 206-233

  Lamberton, Damien ^a  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

Author keywords

American put options; Binomial approximation; Optimal stopping

Indexed keywords

EID: 0032364777     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1027961041     Document Type: Article

References (30)

1. AMIN, K. and KHANNA, A. (1994). Convergence of American option values from discrete to continuous-time financial models. Math. Finance 4 289-304.
2. BAIOCCHI, C. and POZZI, G. A. (1977). Error estimates and free-boundary convergence for a finite-difference discretization of a parabolic variational inequality. RAIRO Analyse numérique/Numerical Analysis 11 315-340.
3. BALLY, V. and TALAY, D. (1996). The law of the Euler scheme for stochastic differential equations (I): convergence rate of the distribution function. Probab. Theory Related Fields 104 43-60.
4. BARLES, G., BURDEAU, J., ROMANO, M. and SANSŒN, N. (1993). Estimation de la frontière libre des options américaines au voisinage de l'échéance. C.R. Acad Sci. Paris Sér. I 316 171-174.
5. BARLES, G., BURDEAU, J., ROMANO, M. and SANSŒN, N. (1995). Critical stock price near expiration. Math. Finance 5 77-95.
6. BENSOUSSAN, A. and LIONS, J. L. (1982). Applications of Variational Inequalities in Stochastic Control. North-Holland, Amsterdam.
7. BRENNAN, M. J. and SCHWARTZ, E. S. (1977). The valuation of the American put option. Journal of Finance 32 449-462.
8. BROADIE, M. and DETEMPLE, J. (1995). American option valuation: new bounds, approximations, and a comparison of existing methods. Review of Financial Studies 9 1211-1250.
9. CARVERHILL, A. P. and WEBBER, N. (1990). American options: theory and numerical analysis. In Options: Recent Advances in Theory and Practice. Manchester Univ. Press.
10. COX, J., ROSS, S. and RUBINSTEIN, M. (1979). Option pricing: a simplified approach. J. Financial Econ. 7 229-263.
11. FRIEDMAN, A. (1975). Parabolic variational inequalities in one space dimension and smoothness of the free boundary. J. Funct. Anal. 18 151-176.
12. JAILLET, P., LAMBERTON, D. and LAPEYRE, B. (1990). Variational inequalities and the pricing of American options. Acta Appl. Math. 1221 263-289.
13. JARROW, R. and RUDD, A. (1983). Option Pricing. Dow Jones-Irwin, Homewood, IL.
14. KARATZAS, I. (1988). On the pricing of American options. Appl. Math. Optim. 17 37-60.
15. KARATZAS, I. (1989). Optimization problems in the theory of continuous trading. SIAM J. Control Optim. 27 1221-1259.
16. KIM, I. J. (1990). The analytic valuation of American options. Review of Financial Studies 3 547-572.
17. KINDERLEHRER, D. and STAMPACCHIA, G. (1980). An introduction to variational inequalities and their applications. Academic Press, New York.
18. KLOEDEN, P. E. and PLATEN, E. (1992). Numerical Solution of Stochastic Differential Equations. Springer, New York.
19. KUSHNER, H. J. (1977). Probability Methods for Approximations in Stochastic Control and for Elliptic Equations. Academic Press, New York.
20. LAMBERTON, D. (1995). Critical price for an American option near maturity. In Seminar on Stochastic Analysis (E. Bolthausen, M. Dozzi and F. Russo, eds.) Progress in Probability 36 353-358. Birkhäuser, Boston.
21. LAMBERTON, D. (1997). American options. In Statistics and Finance (D. Hand and S. Jacka, eds.). Edward Arnold, London. To appear.
22. LAMBERTON, D. and PAGÈS, G. (1990). Sur l'approximation des réduites. Ann. Inst. H. Poincaré Probab. Statist. 26 331-355.
23. LEISEN, D. P. J. and REIMER, M. (1996). Binomial models for option valuation. Examining and improving convergence. Applied Mathematical Finance 3 319-346.
24. MILSHTEIN, G. N. (1985). Weak approximation of solutions of systems of stochastic differential equations. Theory Probab. Appl. 30 750-766.
25. MYNENI, R. (1992). The pricing of the American option. Ann. Appl. Probab. 2 1-23.
26. RENDLEMAN, R. and BARTTER, B. (1979). Two-State option pricing. Journal of Finance 34 1093-1110.
27. SHIRYAEV, A. N. (1984). Probability. Springer, New York.
28. TALAY, D. (1986). Discrétisation d'une E.D.S. et calcul approché d'espérances de fonctionnelles de la solution. Mathematical Modelling and Numerical Analysis 20 141-179.
29. TALAY, D. and TUBARO, L. (1990). Expansion of the global error for the numerical schemes solving stochastic differential equations. Stochastic Anal. Appl. 8 94-120.
30. TIAN, Y. (1993). A modified lattice approach to option pricing. Journal of Futures Markets 13 563-577.