Capturing the volatility smile of options on high-tech stocks—A combined GARCH-neural network approach
Tóm tắt
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.
Tài liệu tham khảo
Anders, U., O. Korn, and C. Schmitt. 1999. “Improving the Pricing of Options: A Neural Network Approach.” Centre for European Research (ZEW), Mannheim.
Black, F., and M. Scholes. 1973. “The Pricing of Options and Corporate Liabilities.”Journal of Political Economy 81: 637–659.
Broomhead, D. S., and D. Lowe. 1988. “Multivariate Functional Interpolation and Adaptive Networks.”Complex Systems 2: 321–355.
Cox, J. C., and S. A. Ross. 1976. “The Valuation of Options for Alternative Stochastic Processes.”Journal of Financial Economics 3: 145–166.
Cox, J. C., S. A. Ross, and M. Rubinstein. 1979. “Option Pricing: A Simplified Approach.”Journal of Financial Economics 7: 229–263.
Engle, R. F. 1982. “Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation.”Econometrica 50: 987–1008.
Fausett, L. 1994.Fundamentals of Neural Networks. New York.
Garcia, R., and R. Gencay. 2000. “Pricing and Hedging Derivative Securities with Neural Networks and Homogeneity Hint.”Journal of Econometrics 94: 93–115.
Gencay, R., and M. Qi. 2001a. “Pricing and Derivative Securities with Neural Networks: Bayesian Regularization, Early Stopping and Bagging.”IEEE Transactions on Neural Networks 12, 726–734.
Haykin, S. 1994.Neural Networks: A Comprehensive Foundation. New York.
Hutchinson, J., Lo, A., and Poggio, T. 1994. “A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks.”Journal of Finance 49: 851–889.
Kohonen, T. 1982. “Self-Organized Formation of Topologically Correct Feature Maps.”Biological Cybernetics 43: 59–69
Merton, R. C. 1976. “Option Pricing When Underlying Stock Returns Are Discontinuous.”Journal of Financial Economics 3: 125–144.
Merton, R. C. 1973. “Theory of Rational Option Pricing.”Bell Journal of Economics and Management Science 4: 141–183.
Moody, J., and C. J. Darkin. 1989. “Fast Learning on Networks of Locally Tuned Processing Unit.”Neural Computation 1: 281–294.
Patterson, D. 1996.Artificial Neural Networks. Singapore: Prentice Hall.
Rubinstein, M. 1985. “Nonparametric Tests of Alternative Option Pricing Models Using All Reported Trades and Quotes of the 30 Most Active CBOE Options Classes from August 23, 1976, through August 21, 1978.”The Journal of Finance 40: 455–480.
Speckt, D. F. 1990. “Probabilistic Neural Networks.”Neural Networks 2: 568–576.