Minqiang Li, Li (2009): Analytical Approximations for the Critical Stock Prices of American Options: A Performance Comparison.
Download (214Kb) | Preview
Many e±cient and accurate analytical methods for pricing American options now exist. However, while they can produce accurate option prices, they often do not give accurate critical stock prices. In this paper, we propose two new analytical approximations for American options based on the quadratic approximation. We compare our methods with existing analytical methods including the quadratic approximations in Barone-Adesi and Whaley (1987) and Barone-Adesi and Elliott (1991), the lower bound approximation in Broadie and Detemple (1996), the tangent approximation in Bunch and Johnson (2000), the Laplace inversion method in Zhu (2006b), and the interpolation method in Li (2008). Both of our methods give much more accurate critical stock prices than all the existing methods above.
|Item Type:||MPRA Paper|
|Original Title:||Analytical Approximations for the Critical Stock Prices of American Options: A Performance Comparison|
|Keywords:||American option; Analytical approximation; Critical stock price|
|Subjects:||C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C63 - Computational Techniques; Simulation Modeling
C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods
G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing
|Depositing User:||Minqiang Li|
|Date Deposited:||15. Sep 2009 00:07|
|Last Modified:||15. Feb 2013 16:07|
AitSahlia, F., Carr, P., 1997. American options: A comparison of numerical methods. In Numerical Methods in Finance, L.C.G. Rogers and D. Talay ed., 67-87, Cambridge University Press, London.
Barone-Adesi, G., 2005. The saga of the American put. Journal of Banking & Finance 29, 2909-2918.
Barone-Adesi, G., Elliott R.J., 1991. Approximations for the values of American options. Stochastic Analysis and Applications 9(2), 115-131.
Barone-Adesi, G., Whaley, R., 1987. E±cient analytical approximation of American option values. Journal of Finance 42, 301-320.
Bjerksund, P., Stensland, G., 1993. Closed form approximation of American options. Scandinavian Journal of Management 9, Suppl., 87-99.
Broadie, M., Detemple, J.B., 1996. American option valuation: New bounds, approximations, and a comparison of existing methods. Review of Financial Studies 9, 1211-1250.
Bunch, D., Johnson, H.E., 2000. The American put option and its critical stock price. Journal of Finance 55(5), 2333-2356.
Carr, P., 1998. Randomization and the American put. Review of Financial Studies 11, 597-626.
Carr, P., Jarrow, R., Myneni, R., 1992. Alternative characterizations of American put options. Mathematical Finance 2, 87-106.
Cox, J.C., Ross, S.A., Rubinstein, M., 1979. Option pricing: A simpli¯ed approach. Journal of Financial Economics 7, 229-264.
Detemple, J.B, 2006. American-style Derivatives: Valuation and Computation. CRC Press, Taylor and Francis Group, London.
Evans, J.D., Kuske, R., Keller, J.B., 2002. American options on assets with dividends near expiry. Mathematical Finance 12, 219-237.
Geske, R., Johnson, H.E., 1984. The American put option valued analytically. Journal of Finance 39, 1511-1524.
Huang, J., Subrahmanyam, M., Yu, G., 1996. Pricing and hedging American options: A recursive integration method. Review of Financial Studies 9, 277-330.
Jacka, S.D., 1991. Optimal stopping and the American put. Mathematical Finance 1, 1-14.
Johnson, H.E., 1983. An analytic approximation for the American put price. Journal of Financial and Quantitative Analysis 18(1), 141-148.
Ju, N., 1998. Pricing an American option by approximating its early exercise boundary as a multi-piece exponential function. Review of Financial Studies 11, 627-646.
Ju, N., Zhong, R., 1999. An approximate formula for pricing American options. Journal of Derivatives 7, 31-40.
Kallast, S., Kivinukk, A., 2003. Pricing and hedging American options using approximations by Kim integral equations. Review of Finance 7, 361-383.
Khaliqa, A.Q.M., Vossb, D.A., Kazmic, S.H.K., 2006. A linearly implicit predictor-corrector scheme for pricing American options using a penalty method approach. Journal of Banking & Finance 30(2), 489-502.
Kim, I.J., 1990. The analytic valuation of American options. Review of Financial Studies 3, 547-572.
Kim I.J., Jang, B-G., 2008. An alternative numerical approach for valuation of American options: A simple iteration method. Working paper, Yonsei University.
Li, M., 2008. Approximate inversion of the Black-Scholes formula using rational functions. European Journal of Operational Research 185(2), 743-759.
Li, M. and K. Lee, 2009. An adaptive successive over-relaxation method for computing the Black-Scholes implied volatility. Quantitative Finance, forthcoming.
Little, T., Pant, V., Hou, C., 2000. A new integral representation of the early exercise boundary for American put options. Journal of Computational Finance 3(3), 73-96.
Longstaff, F.A., Schwartz, E.A., 2001. Valuing American options by simulations: A simple least-squares approach. Review of Financial Studies 14, 113-147.
MacMillan, L.W, 1986. An analytic approximation for the American put prices. Advances in Futures and Options Research 1, 119-139.
McDonald, R.D., Schroder, M.D., 1998. A parity result for American options. Journal of Computational Finance 1, 5-13.
McKean, H.P. Jr., 1965. Appendix: A free boundary problem for the heat equation arising from a problem in mathematical economics. Industrial Management Review 6, 32-39.
Merton, R.C., 1973. Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141-183.
Myneni, R., 1992. The pricing of American option. Annals of Applied Probability 2(1), 1-23.
Pressacco, F., Gaudenzi, M., Zanette, A., Ziani, L., 2008. New insights on testing the e±ciency of methods of pricing and hedging American options. European Journal of Operational Research 185, 235-254.
Samuelson, P.A., 1967. Rational theory of warrant pricing. Industrial Management Review 6, 13-31.
Sullivan, M.A., 2000. Valuing American put options using Gaussian quadrature. Review of Financial Studies 13(1), 75-94.
Van Moerbeke, P., 1976. On optimal stopping and free boundary problems. Archive for Rational Mechanics and Analysis 60, 101-148.
Zhu, S.P., 2006a. An exact and explicit solution for the valuation of American put options. Quantitative Finance 6(3), 229-242.
Zhu, S.P., 2006b. A new analytical-approximation formula for the optimal exercise boundary of American put options. International Journal of Theoretical and Applied Finance 9(7), 1141-1177.