Abstract
In this contribution we propose a two-step simulation procedure that enables to compute the exercise features of American options and analyze the properties of the optimal exercise times and exercise probabilities. The first step of the procedure is based on the calculation of an accurate approximation of the optimal exercise boundary. In particular, we use a smoothed binomial method which effectively reduces the fluctuating behavior of a discrete boundary. In the second step the boundary is used to define a stopping rule which is embodied in a Monte Carlo simulation method. A broad experimental analysis is carried out in order to test the procedure and study the behavior of the exercise features.
Mathematics Subject Classification (2000): 60G40, 60J60, 65C20
Journal of Economic Literature Classification: G13
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References
1. AitShalia, F., Lai, T.L. (1999): A canonical optimal stopping problem for American options and its numerical solution. The Journal of Computational Finance 3(2), 33–52
2. AitShalia, F., Lai, T.L. (2001): Exercise boundaries and efficient approximations to American option prices and hedge parameters. The Journal of Computational Finance 4(4), 85–103
3. Allegretto, W., Barone-Adesi, G., Elliott, R.J. (1995): Numerical evaluation of the critical price and American options. The European Journal of Finance 1, 69–78
4. Barraquand, J., Martineau, D. (1995): Numerical valuation of high dimensional multivariate American securities. Journal of Financial and Quantitative Analysis 30, 383–405
5. Basso, A., Nardon, M., Pianca, P. (2002a): Discrete and continuous time approximations of the optimal exercise boundary of American options. Quaderni 105/02. Dipartimento di Matematica Applicata, Università “Ca' Foscari” di Venezia
6. Basso, A., Nardon, M., Pianca, P. (2002b): An analysis of the effects of continuous dividends on the exercise of American options. Rendiconti per gli Studi Economici Quantitativi 2001, 41–68
7. Boyle, P.P., Broadie, M., Glasserman, P. (2001): Monte Carlo methods for security pricing. In: Jouini, E. et al. (eds.): Option pricing, interest rates and risk management. Cambridge University Press, Cambridge, pp. 185–238
8. Broadie, M., Detemple, J. (1996): American option valuation: new bounds, approximations, and a comparison of existing methods. The Review of Financial Studies 9, 1211–1250
9. Broadie, M., Glasserman, P. (1997): Pricing American-style securities using simulations. Journal of Economic Dynamics and Control 21, 1323–1352
10. Bunch, D.S., Johnson, H. (2000): The American put option and its critical stock price. The Journal of Finance 55, 2333–2356
11. Carr, P. (1998): Randomization and the American put. The Review of Financial Studies 11, 597–626
12. Carr, P., Chesney, M. (1996): American put call symmetry. Working paper. Morgan Stanley, Ney York
13. Carr, P., Jarrow, R., Myneni, R. (1992): Alternative characterizations of American put options. Mathematical Finance 2, 87–106
14. Carriere, J. (1996): Valuation of the early-exercise price of options using simulations and nonparametric regression. Insurance: Mathematics and Economics 19, 19–30
15. Curran, M. (1995): Accelerating American option pricing in lattices. The Journal of Derivatives 3(2), 8–18
16. Cox, J., Rubinstein, M. (1985): Option Markets, Prentice-Hall. Englewood Cliffs, N.J.
17. Detemple, J. (2001): American options: symmetry properties. In: Jouini, E. etz al. (eds.): Option pricing, interest rates and risk management. Cambridge University Press, Cambridge, pp. 67–104
18. Gao, B., Huang, J.-Z., Subrahmanyam, M. (2000): The valuation of American barrier options using the decomposition technique. Journal of Economic Dynamics and Control 24, 1783–1827
19. Geske, R., Shastri, K. (1985): The early exercise of American puts. Journal of Banking and Finance 9, 207–219
20. Huang, J., Subrahmanyam, M., Yu, G. (1996): Pricing and hedging American options: a recursive integration method. The Review of Financial Studies 9, 277–300
21. Jacka, S.D. (1991): Optimal stopping and the American put. Mathematical Finance 1, 1–14
22. Ju, N. (1998): Pricing an American option by approximating its early exercise boundary as a multipiece exponential function. The Review of Financial Studies 11, 627–646
23. Karatzas, I., Shreve, S. (1998): Methods of mathematical finance. Springer, New York
24. Kim, I.J. (1990): The analytic valuation of American options. The Review of Financial Studies 3, 547–572
25. Kim, I.J., Byun, S.J. (1994): Optimal exercise boundary in a binomial option pricing model. Journal of Financial Engineering 3, 137–158
26. Little, T., Pant, V., Hou, C. (2000): A new integral representation of the early exercise boundary for American put options. The Journal of Computational Finance 3(3), 73–96
27. Longstaff, F., Schwartz, E. (2001): Valuing American options by simulation: a simple least-squares approach. The Review of Financial Studies 14, 113–147
28. McDonald, R.L., Schroder, M.D. (1998): A parity result for American options. The Journal of Computational Finance 1(3), 5–13
29. Meyer, G.H. (2002): Numerical investigation of early exercise in American puts with discrete dividends. The Journal of Computational Finance 5(2), 37–53
30. Myneni, R. (1992): The pricing of the American option. The Annals of Applied Probability 2, 1–23
31. Omberg, E. (1987): The valuation of American put options with exponential exercise policies. Advances in Futures and Options Research 2, 117–142
32. Sullivan, M.A. (2000): Valuing American put options using Gaussian quadrature. The Review of Financial Studies 13, 75–94
33. Tilley, J.A. (1993): Valuing American options in a path simulation model. Transactions of the Society of Actuaries 45, 499–520
34. van Moerbeke, P. (1976): On optimal stopping and free boundary problems. Archive for Rational Mechanics and Analisis 60, 101–148
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Basso, A., Nardon, M. & Pianca, P. A two-step simulation procedure to analyze the exercise features of American options. Decisions Econ Finan 27, 35–56 (2004). https://doi.org/10.1007/s10203-004-0045-2
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DOI: https://doi.org/10.1007/s10203-004-0045-2