The random-time binomial model

Journal of Economic Dynamics and Control

Volumn 23, Issue 9-10, 1999, Pages 1355-1386

  Leisen, Dietmar P J ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

Binomial model; Lattice approach; Option valuation

Indexed keywords

EID: 0033193730     PISSN: 01651889     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0165-1889(98)00077-3     Document Type: Article

References (39)

1. Amin K.I. Jump diffusion option valuation in discrete time. The Journal of Finance. 43:1993;1833-1863.
2. Ball A., Torous W. On jumps in common stock prices and their impact on call option pricing. The Journal of Finance. 40:1985;155-173.
3. Black F., Scholes M. The pricing of options and corporate liabilities. Journal of Political Economy. 81:1973;637-659.
4. Boyle P.P. Options: a Monte Carlo approach. Journal of Financial Economics. 4:1976;323-338.
5. Boyle P.P. Option valuation using a three-jump process. International Options Journal. 3:1988;7-12.
6. Boyle P.P., Broadie M., Glasserman P. Monte-Carlo methods for security pricing. Journal of Economic Dynamics and Control. 21:1997;323-338.
7. Broadie, M., Glasserman, P., 1997. A stochastic mesh method for pricing high-dimensional American options. Discussion paper, Columbia University.
8. Carr, P., 1997. Randomization and the American put. Review of Financial Studies, to appear.
9. Carr, P., Faguet, D., 1996. Valuing finite-lived options as perpetuals. Working paper, Cornell University.
10. Carr, P., Jarrow, R., Myneni, R., 1992. Alternative characterization of American put options. Mathematical Finance, 2.
11. Chow, Y., Robbins, H., Siegmund, D., 1991. The Theory of Optimal Stopping. Dover Publications, New York.
12. Cox J.C., Ross S.A., Rubinstein M. Option pricing: a simplified approach. Journal of Financial Economics. 7:1979;229-263.
13. Dengler, H., Jarrow, R., 1997. Option pricing using a binomial model with random time steps (A formal model of gamma hedging). Review of Derivatives Research, 107-138.
14. Ethier, S.N., Kurtz, T., 1986. Markov Processes: Characterization and Convergence. Wiley, New York.
15. Feller, W., 1966. An Introduction to Probability Theory and its Applications, vol. 2. Wiley, New York.
16. Föllmer, H., Sondermann, D., 1986. Hedging of non-redundant contingent claims. In: Hildenbrand, W., Mas-Colell, A. (Eds.), Contributions to Mathematical Economics, Chapter 12. North-Holland, Amsterdam, pp. 205-223.
17. Harrison J.M., Kreps D.M. Martingales and arbitrage in multiperiod securities markets. Journal of Economic Theory. 20:1979;381-408.
18. Harrison J.M., Pliska S.R. Martingales and stochastic integrals in the theory of continous trading. Stochastic Processes and their Applications. 11:1981;215-260.
19. He, H., 1990. Convergence from discrete- to continuous-time contingent claims prices. The Review of Financial Studies 3(4).
20. Jacod, J., Shiryaev, A.N., 1987. Limit Theorems for Stochastic Processes. Springer, Berlin.
21. Jarrow R., Rosenfeld E. Jumps risks and the intertemporal capital asset pricing model. Journal of Business. 57:1984;337-351.
22. Jarrow, R., Rudd, A., 1983. Option Pricing. Irwin, Homewood.
23. Jorion P. On jump processes in the foreign exchange and stock markets. The Review of Financial Studies. 4:1988;427-445.
24. Kloeden, P.E., Platen, E., 1992. Numerical Solution of Stochastic Differential Equations. Springer, Berlin.
25. Lamberton D., Pagès G. Sur l'approximation des réduites. Annales de l'Institut Henri Poincaré - Probabilité Statistique. 26:1990;331-355.
26. Leisen D.P. Pricing the American put option: a detailed convergence analysis for binomial models. Journal of Economic Dynamics and Control. 22:1998;1419-1444.
27. Leisen D.P., Reimer M. Binomial models for option valuation - examining and improving convergence. Applied Mathematical Finanace. 3:1996;319-346.
28. Merton R.C. Theory of rational option pricing. Bell Journal of Economics and Management Science. 4:1973;141-183.
29. Merton R.C. Option pricing when underlying stock returns are discontinous. Journal of Financial Economics. 3:1976;125-144.
30. Meyer, G.H., Van der Hoek, J., 1997. The valuation of American put options with the method of lines. Advances in Futures and Options Research, vol. 9. JAI Press, pp. 265-285.
31. Mulinacci S., Pratelli M. Functional Convergence of Snell envelopes; applications to American options approximations. Finance and Stochastics. 2:1998;311-327.
32. Myneni R. The pricing of the American option. The Annals of Applied Probability. 2:1992;1-23.
33. Nelson D.B., Ramaswamy K. Simple binomial processes as diffusion approximations in financial models. The Review of Financial Studies. 3:1990;393-430.
34. Rendleman R.J., Bartter B.J. Two-state option pricing. The Journal of Finance. 34:1979;1093-1110.
35. Rogers C., Stapleton E. Fast accurate binomial pricing. Finance and Stochastics. 2:1998;3-17.
36. Rust J. Using randomization to break the curse of dimensionality. Econometrica. 65:1997;487-516.
37. Sondermann D. Currency options: hedging and social value. European Economic Review. 31:1987;246-256.
38. Tian Y. A modified lattice approach to option pricing. Journal of Futures Markets. 13:1993;563-577.
39. Van Moerbeke P.L. On optimal stopping and free boundary problems. Archive Rational Mechanical Analysis. 60:1976;101-148.