Hedging derivative securities with genetic programming

One of the most recent applications of GP to finance is to use genetic programming to derive option pricing formulas. Earlier studies take the Black–Scholes model as the true model and use the artificial data generated by it to train and to test GP. The aim of this paper is to provide some initial evidence of the empirical relevance of GP to option pricing. By using the real data from S&P 500 index options, we train and test our GP by distinguishing the case in-the-money from the case out-of-the-money. Unlike most empirical studies, we do not evaluate the performance of GP in terms of its pricing accuracy. Instead, the derived GP tree is compared with the Black–Scholes model in its capability to hedge. To do so, a notion of tracking error is taken as the performance measure. Based on the post-sample performance, it is found that in approximately 20% of the 97 test paths GP has a lower tracking error than the Black–Scholes formula. We further compare our result with the ones obtained by radial basis functions and multilayer perceptrons and one-stage GP. Copyright  1999 John Wiley & Sons, Ltd.

[1]  M. Rubinstein..  Implied Binomial Trees , 1994 .

[2]  John R. Koza,et al.  Genetic programming - on the programming of computers by means of natural selection , 1993, Complex adaptive systems.

[3]  Shu-Heng Chen,et al.  Option pricing with genetic algorithms: separating out-of-the-money from in-the-money , 1997, 1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335).

[4]  E. Barucci,et al.  Neural Networks for Contingent Claim Pricing via the Galerkin Method , 1997 .

[5]  Gerald J. Sussman,et al.  Structure and interpretation of computer programs , 1985, Proceedings of the IEEE.

[6]  J. Hull.  Options, futures, and other derivative securities , 1989 .

[7]  Alan L. Tucker.  Financial Futures, Options, and Swaps , 1990 .

[8]  R. Chou,et al.  ARCH modeling in finance: A review of the theory and empirical evidence , 1992 .

[9]  Günter Rudolph,et al.  Convergence of evolutionary algorithms in general search spaces , 1996, Proceedings of IEEE International Conference on Evolutionary Computation.

[10]  陳樹衡,et al.  Option Pricing with Genetic Programming , 1998 .

[11]  P. Williamson,et al.  The Economics Of Financial Markets , 1996 .

[12]  M. Rubinstein..  Nonparametric tests of alternative option pricing models using all reported trades and quotes on the , 1985 .

[13]  陳樹衡.  Modeling Volatility with Genetic Programming: A First Report , 1998 .

[14]  M.N. Sastry,et al.  Structure and interpretation of computer programs , 1986, Proceedings of the IEEE.

[15]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[16]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[17]  A. Lo,et al.  Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test , 1987 .