Capturing the volatility smile of options on high-tech stocks—A combined GARCH-neural network approach

A slight modification of the standard GARCH equation results in a good modeling of historical volatility. Using this generated GARCH volatility together with the inputs: spot price divided by strike, time to maturity, and interest rate, a generated Neural Network results in significantly better pricing performance than the Black Scholes model. A single Neural Network for each individual high-tech stock is able to adapt to the market inherent volatility distortion. A single Network for all tested high-tech stocks also results in significantly better pricing performance than the Black-Scholes model.

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

[2]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[3]  S. Ross,et al.  The valuation of options for alternative stochastic processes , 1976 .

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

[5]  S. Ross,et al.  Option pricing: A simplified approach☆ , 1979 .

[6]  R. Engle.  Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation , 1982 .

[7]  T. Kohonen.  Self-organized formation of topographically correct feature maps , 1982 .

[8]  David S. Broomhead,et al.  Multivariable Functional Interpolation and Adaptive Networks , 1988, Complex Syst..

[9]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[10]  Donald F. Specht,et al.  Probabilistic neural networks , 1990, Neural Networks.

[11]  Donald F. Specht,et al.  A general regression neural network , 1991, IEEE Trans. Neural Networks.

[12]  Youngohc Yoon,et al.  Predicting stock price performance: a neural network approach , 1991, Proceedings of the Twenty-Fourth Annual Hawaii International Conference on System Sciences.

[13]  Laurene V. Fausett,et al.  Fundamentals Of Neural Networks , 1993 .

[14]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[15]  Ulrich Anders,et al.  Improving the pricing of options: a neural network approach , 1998 .

[16]  Yoshua Bengio,et al.  Pricing and Hedging Derivative Securities with Neural Networks and a Homogeneity Hint , 2000 .

[17]  Min Qi,et al.  Pricing and hedging derivative securities with neural networks: Bayesian regularization, early stopping, and bagging , 2001, IEEE Trans. Neural Networks.