Abstract
In this paper, we use Genetic Programming, an optimization technique based on the principles of natural selection, to price financial contingent claims. Compared to the traditional arbitrage-based approach, this technique is useful when the underlying asset dynamics are unknown or when the pricing equations are too complicated to solve analytically. Comparing to other established data-driven option pricing techniques such as neural networks, implied binomial trees, etc., genetic programming has the advantage of not restricting the structure of the pricing formulas. In addition, because it is very easy to incorporate existing analytical pricing formulas into the evolutionary process, genetic programming can be applied in combination with existing pricing methods. In this paper, we show that genetic programming can recover Black-Sholes formula from a simulated data sample of fairly small size. The application to S&P 500 futures options also show promising results.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ait-Sahalia, Y. and A. Lo, (1995). “Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices,” National Bureau of Economic Research Working Paper, 5251.
Allen, F. and R. Karjalainen, (2000). “Using Genetic Algorithms to Find Technical Trading Rules,” Journal of Financial Economics, 51, 245–271.
Andrews, M. and R. Prager, (1994). “Genetic Programming for the Acquisition of Double Auction Market Strategies,” In K.E. Kinnear (Ed.), Advances in Genetic Programming, Cambridge, MA: MIT Press.
Arifovic, J. (1994). “Genetic Algorithm Learning and the Cobweb Model,” Journal of Economic Dynamics and Control, 18, 3–28.
Arifovic, J. (1996). “The Behavior of the Exchange Rate in the Genetic Algorithm and Experimental Economics,” Journal of Political Economy, 104, 510–541.
Black, F., E. Derman, and W. Troy, (1990). “A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options,” Financial Analysts Journal, 46(Jan./Feb.), 33–39.
Black, F. and M. Scholes (1973). “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy, 81, 637–659.
Derman, E. and I. Kani (1994). “Riding on the Smile,” RISK 7, February, 32–39.
Dupire, B. (1994). “Pricing with S Smile,” RISK 7, January, 18–20.
Heath, D., R. Jarrow, and A. Morton (1992). “Bond Pricing and the Term Structure of Interest Rates: a New Methodology for Contingent Claims Evaluation,” Econometrica, 60, 77–105.
Ho, T.-H. (1996). “Finite Automata Play Repeated Prisoner’s Dilemma with Information Processing Costs,” Journal of Economic Dynamics and Control, 20, 173–207.
Ho, T. S. Y., and S. B. Lee (1986). “Term Structure Movements and Pricing of Interest Rate Claims,” Journal of Finance, 41, 1011–1029.
Holland, J.H. (1962). “Outline for a Logical Theory of Adaptive Systems,” Journal of the Association for Computing Machinery, 3, 297–314.
Holland, J. H. (1975). Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence, Ann Arbor, MI: University of Michigan Press.
Hull, J. and A. White (1993). “One-Factor Interest-Rate Models and the Valuation of Interest-Rate Derivative Securities,” Journal of Financial and Quantitative Analysis, 28, 235–254.
Hutchinson, J. M., A. W. Lo, and T. Poggio (1994). “A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks,” Journal of Finance, 851–889.
Jackwerth, J. C. and M. Rubinstein (1996). “Recovering Probability Distributions from Option Prices,” Journal of Finance, 51, 1611–1652.
Koza, J. R. (1992). Genetic Programming: on the Programming of Computers by Means of Natural selection, Cambridge, MA: MIT Press.
Koza, J. R. (1994). Genetic Programming II: Automatic Discovery of Reusable Programs, Cambridge, MA: MIT Press.
Merton, R. (1973). “Rational Theory of Option Pricing,” Bell Journal of Economics and Management Science, 4, 141–183.
Neely, C., P. Weiler, and R. Dittmar (1997). “Is Technical Analysis in the Foreign Exchange Market Profitable? A Genetic Programming Approach,” Journal of Financial and Quantitative Analysis, 32, 405–426.
Noe, T. H., and L. Pi (2000). “Genetic Algorithm, Learning, and the Dynamics of Corporate Takeovers,” Journal of Economic Dynamics and Control, forthcoming.
Rubinstein, M. (1994). “Implied Binomial Trees,” Journal of Finance, 49, 771–818.
Stutzer, M. (1996). “A Simple Nonparametric Approach to Derivative Security Valuation,” Journal of Finance, 51, 1633–1652.
Wang, J. (2000). “Trading and Hedging in S&P 500 Spot and Futures Markets Using Genetic Programming,” Journal of Futures Markets, forthcoming.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer Science+Business Media New York
About this chapter
Cite this chapter
Noe, T.H., Wang, J. (2002). The Self-Evolving Logic of Financial Claim Prices. In: Chen, SH. (eds) Genetic Algorithms and Genetic Programming in Computational Finance. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-0835-9_12
Download citation
DOI: https://doi.org/10.1007/978-1-4615-0835-9_12
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-5262-4
Online ISBN: 978-1-4615-0835-9
eBook Packages: Springer Book Archive