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Robust Artificial Neural Networks for Pricing of European Options

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Abstract

The option pricing ability of Robust Artificial Neural Networks optimized with the Huber function is compared against those optimized with Least Squares. Comparison is in respect to pricing European call options on the S&P 500 using daily data for the period April 1998 to August 2001. The analysis is augmented with the use of several historical and implied volatility measures. Implied volatilities are the overall average, and the average per maturity. Beyond the standard neural networks, hybrid networks that directly incorporate information from the parametric model are included in the analysis. It is shown that the artificial neural network models with the use of the Huber function outperform the ones optimized with least squares.

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References

  • Ackert, L.F. and Tian, Y.S. (2001). Efficiency in index option markets and trading in stock baskets. Journal of Banking and Finance, 25, 1607–1634.

    Article  Google Scholar 

  • Andersen, T.G., Benzoni, L. and Lund, J. (2002). An empirical investigation of continuous-time equity return models. Journal of Finance, 57(3), 1239–1276.

    Article  Google Scholar 

  • Andreou, P.C., Charalambous, C. and Martzoukos, S.H. (2005). Pricing and trading European options by combining artificial neural networks and parametric models with implied parameters. To be published in the European Journal of Operational Research.

  • Bakshi, G., Cao, C. and Chen, Z. (1997). Empirical performance of alternative options pricing models. Journal of Finance, 52(5), 2003–2049.

    Article  Google Scholar 

  • Bakshi, G., Cao, C. and Chen, Z. (2000). Pricing and hedging long-term options. Journal of Econometrics, 94, 277–318.

    Article  Google Scholar 

  • Bandler, W.J., Chen, H.S., Biernacki, M.R., Gao, L. and Madsen, K. (1993). Huber optimization of circuits: A robust approach. IEEE Transactions on Microwave Theory and Techniques, 41(12), 2279–2287.

    Article  Google Scholar 

  • Bates, D.S. (1991). The Crash of '87: Was it expected? The evidence from options markets. Journal of Finance, 46(3), 1009–1044.

    Article  Google Scholar 

  • Bates, D.S. (1996). Jumps and stochastic volatility: Exchange rate processes implicit in Deutsche mark options. The Review of Financial Studies, 9(1), 69–107.

    Article  Google Scholar 

  • Bates, D.S. (1996b). Testing Option Pricing Models. In G.S. Maddala and C.R. Rao, (eds.), Statistical Methods in Finance (Handbook of Statistics, v. 14). Amsterdam, Elsevier, 567–611.

    Chapter  Google Scholar 

  • Bates, D.S. (2003). Empirical option pricing: A retrospection. Journal of Econometrics, 116, 387–404.

    Article  MathSciNet  Google Scholar 

  • Bishop, M.C. (1995). Neural Networks for Pattern Recognition. Oxford University Press.

  • Black, F. and Scholes, M. (1972). The valuation of option contracts and a test of market efficiency. The Journal of Finance, 27, 399–417.

    Article  Google Scholar 

  • Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.

    Article  Google Scholar 

  • Black, F. and Scholes, M. (1975). Fact and fantasy in the use of options. The Financial Analysts Journal, 31, 36–41 and 61–72.

    Google Scholar 

  • Canica, L. and Figlewski, S. (1993). The informational content of implied volatility. The Review of Financial Studies, 6(3), 659–681.

    Article  Google Scholar 

  • Chang, W.X. (2005). Computation of Huber's M-estimated for a block-angular regression problem. Forthcoming in the Computational Statistics & Data Analysis.

  • Chiras, D.P. and Manaster, S. (1978). The informational content of option prices and a test of market efficiency. Journal of Financial Economics, 6, 213–234.

    Article  Google Scholar 

  • Cont, R. and Fonseca, J. (2002). Dynamics of implied volatility surfaces. Quantitative Finance, 2, 45–60.

    Article  MathSciNet  Google Scholar 

  • Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of Control, Signal and Systems, 2, 303–314.

    Article  Google Scholar 

  • Day, T.E. and Lewis, C.M. (1988). The behavior of the volatility implicit in the prices of stock index options. Journal of Financial Economics, 22, 103–122.

    Article  Google Scholar 

  • Devabhaktuni, V., Yagoub, M.C.E., Fang, Y., Xu, J. and Zhang, Q.J. (2001). Neural networks for microwave modeling: Model development issues and nonlinear modeling techniques. International Journal of RF and Microwave CAE, 11, 4–21.

    Article  Google Scholar 

  • Dumas, B., Fleming, J. and Whaley, R. (1995). Implied volatility smiles: Empirical tests. Journal of Finance, LIII(6), 2059–2106.

    Google Scholar 

  • Ederington, L. and Guan, W. (2005). The information frown in option prices. Journal of Banking and Finance, 29(6), 1429–1457.

    Article  Google Scholar 

  • Franses, H.P., Kloek, T. and Lucas, A. (1999). Outlier robust analysis of long-run marketing effects for weekly scanning data. Journal of Econometrics, 89, 293–315.

    Article  Google Scholar 

  • Galai, D. (1977). Tests of market efficiency of the Chicago Board Options Exchange. The Journal of Business, 50, 167–197.

    Article  Google Scholar 

  • Garcia, R. and Gencay, R. (2000). Pricing and hedging derivative securities with neural networks and a homogeneity hint. Journal of Econometrics, 94, 93–115.

    Article  Google Scholar 

  • Hagan, M.T., Demuth, H. and Beale, M. (1996). Neural Network Design. PWS Publishing Company.

  • Hagan, M.T. and Menhaj, M. (1994). Training feedforward networks with the Marquardt algorithm. IEEE Transactions on Neural Networks, 5(6) 989–993.

    Article  Google Scholar 

  • Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J. and Stahel, P.J. (1986). Robust Statistics: The Approach Based on Influenced Functions. Wiley, New York.

    Google Scholar 

  • Haykin, S. (1999). Neural Netwroks – A Comprehensive Foundation, 2nd ed., Prentice Hall.

  • Huber, P. (1981). Robust Statistics. Wiley, New York.

    Google Scholar 

  • Hutchison, J.M., Lo, A.W. and Poggio, T. (1994). A nonparametric approach to pricing and hedging derivative securities via learning networks. Journal of Finance, 49(3), 851–889.

    Article  Google Scholar 

  • Jabr, R.A. (2004). Power system Huber M-estimation with equality and inequality constraints. Forthcoming in Electric Power Systems Research.

  • Kamara, A. and Miller, T.W. (1995). Daily and intradaily tests of put-call parity. Journal of Financial and Quantitative Analysis, 30, 519–539.

    Article  Google Scholar 

  • Koenker, R. (1982). Robust Methods in Econometrics. Econometric Reviews, 1(2), 213–255.

    Article  Google Scholar 

  • Krishnakumar, J. and Ronchetti, E. (1997). Robust estimators for simultaneous equations models. Journal of Econometrics, 78, 295–314.

    Article  Google Scholar 

  • Lajbcygier P., Boek C., Palaniswami, M. and Flitman, A. (1996). Comparing conventional and artificial neural network models for the pricing of options on futures. Neurovest Journali, 4(5), 16–24.

    Google Scholar 

  • Lajbcygier, P., Flitman, A., Swan, A. and Hyndman, R. (1997). The pricing and trading of options using a hybrid neural network model with historical volatility. Neurovest Journal, 5(1) 27–41.

    Google Scholar 

  • Latane, H.A. and Rendleman, R.J. Jr. (1976). Standard deviations of stock price ratios implied in option prices. The Journal of Financei, 31(2), 369–381.

    Article  Google Scholar 

  • Lim, G.C., Lye, J.N., Martin, G.M. and Martin, V.L. (1997). Jump models and higher moments. In J. Creedy, V. L. Martin (eds.), Nonlinear Economic Models. Cross-sectional, Time Series and Neural Networks Applications. Edward Elgar Publishing, Inc., Lyme NH, US.

  • Long, D.M. and Officer, D.T. (1997). The Relation Between Option Mispricing and Volume in the Black-Scholes Option Model. Journal of Financial Research, XX(1), 1–12.

    Google Scholar 

  • Lye, J.N. and Martin, V.L. (1993). Robust Estimation, Non-normalities and Generalized Exponential Distributions. Journal of the American Statistical Association, 88 (421), 253–259.

    Article  Google Scholar 

  • Morgenthaler, S. (1990). Fitting Redescenting M-estimators in Regression. In K.D. Lawrence and J.L. Arthur (eds.) Robust Regression, Dekker, NY. 105–128.

    Google Scholar 

  • Ortelli, C. and Trojani, F. (2005). Robust efficient method of moments. The Journal of Econometrics, 128(1), 69–97.

    Article  Google Scholar 

  • Rousseeuw, P. and Yohai, V.J. (1984). Robust Regression by Means of S-estimators. Robust and Nonlinear time series analysis. Lecture Notes in Statistics, 26, 256–272. Springer, NY.

  • Rubinstein, M. (1985). Nonparametric tests of alternative option pricing models using all reported trades and quotes on the 30 most active CBOE option classes from August 23, 1976 through August 31, 1978. The Journal of Finance, XL, 455–480.

  • Schittenkopf, C. and Dorffner, G. (2001). Risk-neutral density extraction from option prices: Improved pricing with mixture density networks. IEEE Transactions on Neural Networks, 12(4), 716–725.

    Article  Google Scholar 

  • Tsay, S.R. (2002). Analysis of Financial Time Series, Wiley Series in Probability and Statistics.

  • Watson, P. and Gupta, K.C. (1996). EM-ANN models for microstript vias and interconnected in multilayer circuits. IEEE Trans., Microwave Theory and Techniques, 44, 2495–2503.

    Article  Google Scholar 

  • Whaley, R.E. (1982). Valuation of American call Options on dividend-paying stocks. The Journal of Financial Economics, 10, 29–58.

    Article  Google Scholar 

  • Xi, C., Wang, F., Devabhaktuni, V.K. and Zhang, J.Q. (1999). Huber optimization of neural networks: A robust training method. International Joint Conference on Neural Networks, 1639–1642.

  • Yohai, V.J. (1987). High breakdown-point and high efficiency robust estimates for regression. Annals of Statistics, 15 (2), 642–656.

    Google Scholar 

  • Yao, J., Li, Y. and Tan, C.L. (2000). Option price forecasting using neural networks. The International Journal of Management Science, 28, 455–466.

    Google Scholar 

Download references

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Correspondence to Chris Charalambous.

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JEL Classification: G13, G14

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Andreou, P.C., Charalambous, C. & Martzoukos, S.H. Robust Artificial Neural Networks for Pricing of European Options. Comput Econ 27, 329–351 (2006). https://doi.org/10.1007/s10614-006-9030-x

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