Abstract
Mathematically, the Black-Scholes model of American option pricing is a free boundary problem of partial differential equation. It is well known that this model is a nonlinear problem, and it has no closed form solution. We can only obtain an approximate solution by numerical method, but the precision and stability are hard to control, because the singularity at the exercise boundary near expiration date has a great effect on precision and stability for numerical method. We propose a new numerical method, FDA method, to solve the American option pricing problem, which combines advantages the Semi-Analytical Method and the Front-Fixed Difference Method. Using the FDA method overcomes the difficulty resulting from the singularity at the terminal of optimal exercise boundary. A large amount of calculation shows that the FDA method is more accurate and stable than other numerical methods.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Black, F., Scholes, M., The pricing of option and corporate liabilities, Journal of Political Economy, 1973, 81(5): 637–659.
Kwok, Y. K., Mathematical Models of Financial Derivatives, Singapore: Springer-Verlag Singapore Pte. Ltd., 1998,
Kim, I. J., The analytic valuation of American puts, Review of Financial Studies, 1990, 3(4): 547–572.
Barone-Ades, G., Whaley, R., Efficient analytic approximation of American option values, The Journal of Finance, 1987, 42(2): 301–320.
Carr, P., Randomization and the American put, The Review of Financial Studies, 1998, 11(3): 597–626.
Jacka, S. D., Optimal stopping and the American put, Mathematical Finance, 1991, 1(1): 1–14.
MacMillan, L. W., Analytic approximation for the American put option, Advances in Futures and Options Research, 1986, 1(1): 119–139.
Bunch, D., Johnson, H., A simple and numerically valuation method for American puts using a modified Geske-Johnson approach, Journal of Finance, 1992, 47(2): 809–816.
Carr, P., Jarrow, R., Myneni, R., Alternative characterizations of American put options, Mathematical Finance, 1992, 87–106.
Geske, R., Johnson, H., The American put option valued analytically, Journal of Finance, 1984, 39(5): 1511–1542.
Omber, E., The valuation of American puts with exponential exercise policies, Advance in Futures and Options Research, 1987, 2(1): 117–142.
Breneen, M. J., Schwartz, E., The valuation of American put options, Journal of Finance, 1977, 32(2): 449–462.
Schwartz, E. S., The valuation of warrants: implementing a new approach, Journal of Financial Economics, 1997, 4(1): 79–93.
Wu, L., Kwok, Y. K., A front-fixed finite difference method for the valuation of American options, Journal of Financial Engineering, 1997, 6(1): 83–98.
Hon, Y. C., Mao, X. Z., A radial basis function method for solving option pricing methods, Journal of Financial Engineering, 1999, 8(1): 31–50.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gu, Y., Shu, J., Deng, X. et al. A new numerical method on American option pricing. Sci China Ser F 45, 181–188 (2002). https://doi.org/10.1360/02yf9016
Received:
Issue Date:
DOI: https://doi.org/10.1360/02yf9016