A Dynamic Hybrid Option Pricing Model by Genetic Algorithm and Black- Scholes Model

Unlike this study focused extensively on trading behavior of option market, those researches were just taken their attention to model-driven option pricing. For example, Black-Scholes (B-S) model is one of the most famous option pricing models. However, the arguments of B-S model are previously mentioned by some pricing models reviewing. This paper following suggests the importance of the dynamic character for option pricing, which is also the reason why using the genetic algorithm (GA). Because of its natural selection and species evolution, this study proposed a hybrid model, the Genetic-BS model which combining GA and B-S to estimate the price more accurate. As for the final experiments, the result shows that the output estimated price with lower MAE value than the calculated price by either B-S model or its enhanced one, Gram-Charlier garch (G-C garch) model. Finally, this work would conclude that the Genetic-BS pricing model is exactly practical.

Authors:

• Yi-Chang Chen
• Shan-Lin Chang
• Chia-Chun Wu

Keywords:

• genetic algorithm
• Genetic-BS
• option pricing model.

References:

[1] F. Black and M. Scholes, "The pricing of options and corporate
liabilities," Journal of Political and Economy, vol. 81, 1973, pp. 637-654.
[2] J-P. Bouchaud and M. Potters, "Welcome to a non-Black-Scholes world,"
Quantitative Finance, vol. 1, no.5, 2001, pp. 482-483.
[3] G. Barone-Adesi, R. F. Engle, and L. Mancini, "A GARCH option pricing
model with filtered historical simulation," Review of Financial Studies,
vol. 21, no. 3, 2008, pp. 1223-1258.
[4] R. Company, E. Navarro, J. R. Pintos, and E. Ponsoda, "Numerical
solution of linear and nonlinear Black-Scholes option pricing equations,"
Computers and Mathematics with Applications archive, vol. 56, no. 3,
2008, pp. 813-821.
[5] S. K. Mitra, "Valuation of nifty options using Black's option pricing
formula," The Icfai Journal of Derivatives Markets, vol. 5, no. 1, 2008,
pp. 50-61
[6] P. Lin and P. Ko, "Portfolio value-at-risk forecasting with GA-based
extreme value theory," Expert Systems with Applications, vol. 36, 2009,
pp. 2503-2512.
[7] H. Chou, D. Chen, and C. Wu, "Valuation and hedging performance of
gram-charlier GARCH option pricing algorithm," Journal of Management
& Systems, vol. 14, no. 1, 2007, pp. 95-119.
[8] N. K. Chidambaran, C. H. J. Lee, and J. Trigueros, "An adaptive
evolutionary approach to option pricing via genetic programming, in:
evolutionary computation in economics and finance, editor: Shu-Hueng
Chen," Springer Verlag, 2002.
[9] J. Holland, "Adaptation in natural and artificial systems," Originally
published by the University of Michigan Press, 1975.
[10] S. H. Chu and S. Freund, "Volatility estimation for stock index options: a
GARCH approach," Quarterly Review of Economics and Finance, Vol.
36, 1996, pp. 431-450.
[11] S.-H. Chen, W.-C. Lee, "Numerical methods in option pricing:
model-driven approach vs. data-driven approach," Society of Industrial
and Applied Mathematics 45th Anniversary Meeting (SIAM'97), 1997.