Journal of Applied Mathematics and Decision Sciences
Volume 2009 (2009), Article ID 179230, 19 pages
doi:10.1155/2009/179230
Research Article

Selecting the Best Forecasting-Implied Volatility Model Using Genetic Programming

Wafa Abdelmalek,1 Sana Ben Hamida,2 and Fathi Abid1

1RU: MODESFI, Faculty of Economics and Business, Road of the Airport Km 4, 3018 Sfax, Tunisia
2Laboratory of Intelligent IT Engineering, Higher School of Technology and Computer Science, 2035 Charguia, Tunisia

Received 29 November 2008; Revised 15 April 2009; Accepted 10 June 2009

Academic Editor: Lean Yu

Copyright © 2009 Wafa Abdelmalek et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, vol. 81, no. 3, pp. 637–654, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. F. Black, “Fact and fantasy in the use of options,” Financial Analysts Journal, vol. 31, pp. 36–41, 1975.
  3. J. Macbeth and L. Merville, “An empirical examination of the Black and Scholes call option pricing model,” Journal of Finance, vol. 34, pp. 1173–1186, 1979. View at Publisher · View at Google Scholar
  4. M. Rubinstein, “Non-parametric test 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,” Journal of Finance, vol. 40, pp. 455–480, 1985. View at Publisher · View at Google Scholar
  5. L. Clewlow and X. Xu, “The dynamics of stochastic volatility,” Working Paper, Financial Options Research Centre, Warwick University, 1993.
  6. X. Xu and S. J. Taylor, “The term structure of volatility implied by foreign exchange options,” Journal of Financial and Quantitative Analysis, vol. 29, no. 1, pp. 57–74, 1994.
  7. J. Duque and D. Paxson, “Implied volatility and dynamic hedging,” The Review of Futures Markets, vol. 13, no. 2, pp. 381–421, 1994.
  8. R. Heynen, “An empirical investigation of observed smile patterns,” The Review of Futures Markets, vol. 13, no. 2, pp. 317–353, 1994.
  9. G. Gemmill, “Did option traders anticipate the crash? Evidence from volatility smiles in the U.K. with U.S. comparisons,” The Journal of Futures Markets, vol. 16, no. 8, pp. 881–897, 1996. View at Publisher · View at Google Scholar
  10. B. Dumas, J. Fleming, and R. E. Whaley, “Implied volatility functions: empirical tests,” Journal of Finance, vol. 53, no. 6, pp. 2059–2106, 1998. View at Publisher · View at Google Scholar
  11. G. M. Constantinides, “Transaction costs and the volatility implied by option prices,” Tech. Rep., University of Chicago, Chicago, Ill, USA, 1998.
  12. R. Bookstaber, Option Pricing and Investment Strategies, Probus, Chicago, Ill, USA, 3rd edition, 1991.
  13. R. F. Engle, “Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation,” Econometrica, vol. 50, no. 4, pp. 987–1007, 1982.
  14. R. C. Merton, “Theory of rational option pricing,” Bell Journal of Economics and Management Science, vol. 4, no. 1, pp. 141–183, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  15. R. C. Merton, “Option pricing when underlying stock returns are discontinuous,” Journal of Financial Economics, vol. 3, no. 1-2, pp. 125–144, 1976. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  16. S. L. Heston, “A closed-form solution for options with stochastic volatility with applications to bond and currency options,” Review of Financial Studies, vol. 6, pp. 327–343, 1993. View at Publisher · View at Google Scholar
  17. I. Ma, T. Wong, T. Sankar, and R. Siu, “Volatility forecasts of the S&P100 by evolutionary programming in a modified time series data mining framework,” in Proceedings of the World Automation Congress (WAC '04), Seville, Spain, June 2004.
  18. J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, The MIT Press, Cambridge, Mass, USA, 1992.
  19. J. H. Holland, Adaptation in Natural and Artificial Systems, The University of Michigan Press, Ann Arbour, Mich, USA, 1975.
  20. L. Kallel, B. Naudts, and A. Rogers, “Theoretical aspects of evolutionary computing,” in Proceedings of the 2nd EvoNet Summer School Held at the University of Antwerp, Springer, Berlin, Germany, September 1999.
  21. E. Tsang, P. Yung, and J. Li, “EDDIE-automation, a decision support tool for financial forecasting,” Decision Support Systems, vol. 37, no. 4, pp. 559–565, 2004. View at Publisher · View at Google Scholar
  22. M. A. Kaboudan, “A measure of time series' predictability using genetic programming applied to stock returns,” Journal of Forecasting, vol. 18, no. 5, pp. 345–357, 1999. View at Publisher · View at Google Scholar
  23. M. Kaboudan, “Extended daily exchange rates forecasts using wavelet temporal resolutions,” New Mathematics and Natural Computing, vol. 1, pp. 79–107, 2005. View at Publisher · View at Google Scholar
  24. G. Zumbach, O. V. Pictet, and O. Masutti, “Genetic programming with syntactic restrictions applied to financial volatility forecasting,” Working Paper, Olsen & Associates Research Institute, 2001.
  25. C. J. Neely and P. A. Weller, “Predicting exchange rate volatility: genetic programming versus GARCH and riskmetrics,” Working Paper, Federal Reserve Bank of St. Louis, May-June 2002.
  26. S. H. Chen and C. H. Yeh, “Using genetic programming to model volatility in financial time series,” in Proceedings of the 2nd Annual Conference on Genetic Programming, pp. 288–306, Morgan Kaufmann, 1997.
  27. I. Ma, T. Wong, and T. Sanker, “An engineering approach to forecast volatility of financial indices,” International Journal of Computational Intelligence, vol. 3, no. 1, pp. 23–35, 2006.
  28. I. Ma, T. Wong, and T. Sankar, “Volatility forecasting using time series data mining and evolutionary computation techniques,” in Proceedings of the 9th Annual Conference on Genetic and Evolutionary Computation (GECCO '07), p. 2262, ACM Press, London, UK, July 2007. View at Publisher · View at Google Scholar
  29. B. J. Christensen and N. R. Prabhala, “The relation between implied and realized volatility,” Journal of Financial Economics, vol. 50, no. 2, pp. 125–150, 1998. View at Publisher · View at Google Scholar
  30. L. H. Ederington and W. Guan, “Is implied volatility an informationally efficient and effective predictor of future volatility?” NBER Working Paper, University of Oklahoma and Delaware State University, 2000.
  31. B. J. Blair, S.-H. Poon, and S. J. Taylor, “Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns,” Journal of Econometrics, vol. 105, no. 1, pp. 5–26, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  32. T. Busch, B. J. Christensen, and M. Ø. Nielsen, “The role of implied volatility in forecasting future realized volatility and jumps in foreign exchange, stock, and bond markets,” CREATES Research Paper 2007-9, Aarhus School of Business, University of Copenhagen, 2007.
  33. W. Cai, A. Pacheco-Vega, M. Sen, and K. T. Yang, “Heat transfer correlations by symbolic regression,” International Journal of Heat and Mass Transfer, vol. 49, no. 23-24, pp. 4352–4359, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  34. S. Gustafson, E. K. Burke, and N. Krasnogor, “On improving genetic programming for symbolic regression,” in Proceedings of IEEE Congress on Evolutionary Computation (CEC '05), D. Corne, et al., Ed., vol. 1, pp. 912–919, IEEE Press, Edinburgh, UK, 2005.
  35. Z. Yin, A. Brabazon, C. O'Sullivan, and M. O'Neil, “Genetic programming for dynamic environments,” in Proceedings of the International Multiconference on Computer Science and Information Technology, pp. 437–446, 2007.
  36. C. J. Corrado and T. W. Miller Jr., “Efficient option-implied volatility estimators,” The Journal of Futures Markets, vol. 16, no. 3, pp. 247–272, 1996. View at Publisher · View at Google Scholar
  37. C. A. Brown, “The volatility structure implied by options on the SPI futures contract,” Australian Journal of Management, vol. 24, no. 2, pp. 115–130, 1999.
  38. S. Borak, M. Fengler, and W. Härdle, “DSFM fitting of implied volatility surfaces. SFB 649,” Discussion Paper 2005-022, Center for Applied Statistics and Economics, Humboldt-Universität zu Berlin, Berlin, Germany, 2005.
  39. R. Heynen, A. Kemma, and T. Vorst, “Analysis of the term structure of implied volatilities,” Journal of Financial and Quantitative Analysis, vol. 29, no. 1, pp. 31–56, 1994. View at Publisher · View at Google Scholar
  40. S. R. Das and R. K. Sundaram, “Of smiles and smirks: a term structure perspective,” Journal of Financial and Quantitative Analysis, vol. 34, no. 2, pp. 211–239, 1999. View at Publisher · View at Google Scholar
  41. G. Skiadopoulos, S. Hodges, and L. Clewlow, “The dynamics of the S&P 500 implied volatility surface,” Review of Derivatives Research, vol. 3, no. 3, pp. 263–282, 2000. View at Publisher · View at Google Scholar
  42. Y. Zhu and M. Avellaneda, “An E-ARCH model for the term structure of implied volatility of FX options,” Applied Mathematical Finance, vol. 4, no. 2, pp. 81–100, 1997. View at Publisher · View at Google Scholar
  43. R. Hafner and M. Wallmeier, “The dynamics of DAX implied volatilities,” Quarterly International Journal of Finance, vol. 1, pp. 1–27, 2001.
  44. M. R. Fengler, W. K. Härdle, and C. Villa, “The dynamics of implied volatilities: a common principal components approach,” Review of Derivatives Research, vol. 6, no. 3, pp. 179–202, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  45. R. W. Lee, “Implied volatility: statistics, dynamics, and probabilistic interpretation,” in Recent Advances in Applied Probability, pp. 1–27, Springer, New York, NY, USA, 2004.
  46. J.-P. Fouque, G. Papanicolaou, R. Sircar, and K. Solna, “Maturity cycles in implied volatility,” Finance and Stochastics, vol. 8, no. 4, pp. 451–477, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  47. R. Cont and J. da Fonseca, “Dynamics of implied volatility surfaces,” Quantitative Finance, vol. 2, no. 1, pp. 45–60, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  48. R. Cont and J. da Fonseca, “Deformation of implied volatility surfaces: an empirical analysis,” in Empirical Science to Financial Fluctuations, H. Takayasu, Ed., pp. 230–239, Springer, Tokyo, Japan, 2001.
  49. R.-M. Gaspar, “Implied volatility and forward price term structures,” ADVANCES Research Center, ISEG, Technical University Lisbon, Lisbon, Portugal, November 2008.
  50. E. Derman and I. Kani, “Riding on a smile,” Risk, vol. 7, no. 2, pp. 32–39, 1994.
  51. C. Corrado and T. Su, “Skewness and kurtosis in S&P500 index returns implied by option prices,” The Journal of Financial Research, vol. 19, no. 2, pp. 175–192, 1996.
  52. J. Hull and A. White, “The pricing of options on assets with stochastic variables,” Journal of Finance, vol. 42, pp. 281–300, 1987.
  53. J. C. Jackwerth and M. Rubinstein, “Recovering probability distributions from option prices,” Journal of Finance, vol. 51, no. 5, pp. 1611–1631, 1996. View at Publisher · View at Google Scholar