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An Adaptive Evolutionary Approach to Option Pricing via Genetic Programming

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  • N. K. Chidambaran
  • Chi-Wen Jevons Lee
  • Joaguin R. Trigueros
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    Abstract

    We propose a methodology of Genetic Programming to approximate the relationship between the option price, its contract terms and the properties of the underlying stock price. An important advantage of the Genetic Programming approach is that we can incorporate currently known formulas, such as the Black-Scholes model, in the search for the best approximation to the true pricing formula. Using Monte Carlo simulations, we show that the Genetic Programming model approximates the true solution better than the Black-Scholes model when stock prices folow a jump-diffusion process. We also show that the Genetic Programming model outperforms various other models in many different settings. Other advantages of the Genetic Programming approach include its robustness to changing environment, its low demand for data, and its computational speed. Since genetic programs are flexible, self-learning and sefl-improving, they are an ideal tool for practitioners.

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    Bibliographic Info

    Paper provided by New York University, Leonard N. Stern School of Business- in its series New York University, Leonard N. Stern School Finance Department Working Paper Seires with number 98-086.

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    Date of creation: Nov 1998
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    Handle: RePEc:fth:nystfi:98-086

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    Postal: U.S.A.; New York University, Leonard N. Stern School of Business, Department of Economics . 44 West 4th Street. New York, New York 10012-1126
    Phone: (212) 998-0100
    Web page: http://w4.stern.nyu.edu/finance/
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    1. Kim, Dongcheol & Kon, Stanley J, 1994. "Alternative Models for the Conditional Heteroscedasticity of Stock Returns," The Journal of Business, University of Chicago Press, vol. 67(4), pages 563-98, October.
    2. Ball, Clifford A & Torous, Walter N, 1985. " On Jumps in Common Stock Prices and Their Impact on Call Option Pricing," Journal of Finance, American Finance Association, vol. 40(1), pages 155-73, March.
    3. Baillie, Richard T. & DeGennaro, Ramon P., 1990. "Stock Returns and Volatility," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(02), pages 203-214, June.
    4. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    5. Dittmar, Robert & Neely, Christopher J & Weller, Paul, 1996. "Is Technical Analysis in the Foreign Exchange Market Profitable? A Genetic Programming Approach," CEPR Discussion Papers 1480, C.E.P.R. Discussion Papers.
    6. Kaushik I. Amin & Robert A. Jarrow, 1992. "Pricing Options On Risky Assets In A Stochastic Interest Rate Economy," Mathematical Finance, Wiley Blackwell, vol. 2(4), pages 217-237.
    7. French, Kenneth R. & Schwert, G. William & Stambaugh, Robert F., 1987. "Expected stock returns and volatility," Journal of Financial Economics, Elsevier, vol. 19(1), pages 3-29, September.
    8. James M. Hutchinson & Andrew W. Lo & Tomaso Poggio, 1995. "A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks," NBER Working Papers 4718, National Bureau of Economic Research, Inc.
    9. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    10. repec:fth:pennfi:70 is not listed on IDEAS
    11. Marimon, Ramon & McGrattan, Ellen & Sargent, Thomas J., 1990. "Money as a medium of exchange in an economy with artificially intelligent agents," Journal of Economic Dynamics and Control, Elsevier, vol. 14(2), pages 329-373, May.
    12. Franklin Allen & Risto Karjalainen, . "Using Genetic Algorithms to Find Technical Trading Rules (Revised: 20-95)," Rodney L. White Center for Financial Research Working Papers 20-93, Wharton School Rodney L. White Center for Financial Research.
    13. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
    14. MacBeth, James D & Merville, Larry J, 1980. " Tests of the Black-Scholes and Cox Call Option Valuation Models," Journal of Finance, American Finance Association, vol. 35(2), pages 285-301, May.
    15. Black, Fischer & Scholes, Myron S, 1972. "The Valuation of Option Contracts and a Test of Market Efficiency," Journal of Finance, American Finance Association, vol. 27(2), pages 399-417, May.
    16. Galai, Dan, 1977. "Tests of Market Efficiency of the Chicago Board Options Exchange," The Journal of Business, University of Chicago Press, vol. 50(2), pages 167-97, April.
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