Table of Contents Author Guidelines Submit a Manuscript
Advances in Decision Sciences
Volume 2010, Article ID 598103, 15 pages
http://dx.doi.org/10.1155/2010/598103
Research Article

Implications of Parameter Uncertainty on Option Prices

Division of Mathematical Statistic, Centre for Mathematical Sciences, Lund University, P.O. Box 118, 22100 Lund, Sweden

Received 7 September 2009; Accepted 13 February 2010

Academic Editor: Henry Schellhorn

Copyright © 2010 Erik Lindström. 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. H. Madsen and J. Holst, Modelling Non-Linear and Non-Stationary Time Series, Department of Mathematical Modelling, The Technical University of Denmark, 1999.
  2. F. Black and M. Scholes, “The pricing of options and corporate liabilities,” Journal of Political Economy, vol. 81, pp. 637–659, 1973. View at Google Scholar
  3. 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 Google Scholar · View at Scopus
  4. 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 Google Scholar
  5. D. Bates, “Jumps and stochastic volatility: the exchange rate processes implicit in Deutchemark options,” Review of Financial Studies, vol. 9, pp. 69–107, 1996. View at Google Scholar
  6. D. B. Madan and E. Seneta, “The variance gamma (VG) model for share market returns,” The Journal of Business, vol. 63, pp. 511–524, 1990. View at Google Scholar
  7. O. E. Barndorff-Nielsen, “Processes of normal inverse Gaussian type,” Finance and Stochastics, vol. 2, no. 1, pp. 41–68, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. P. Carr, H. Geman, D. B. Madan, and M. Yor, “The fine structure of asset returns: an empirical investigation,” The Journal of Business, vol. 75, no. 2, pp. 305–332, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. P. Carr and L. Wu, “Time-changed Lévy processes and option pricing,” Journal of Financial Economics, vol. 71, no. 1, pp. 113–141, 2004. View at Publisher · View at Google Scholar · View at Scopus
  10. P. Carr and L. Wu, “Stochastic skew in currency options,” Journal of Financial Economics, vol. 86, no. 1, pp. 213–247, 2007. View at Publisher · View at Google Scholar · View at Scopus
  11. L. Edgerington and W. Guan, “Why are those options smiling?” Journal of Derivatives, vol. 10, no. 2, pp. 9–34, 2002. View at Google Scholar
  12. I. Peña, G. Rubio, and G. Serna, “Why do we smile? On the determinants of the implied volatility function,” Journal of Banking & Finance, vol. 23, pp. 1151–1179, 1999. View at Google Scholar
  13. J. C. Hull, Options, Futures, and Other Derivative Securities, Prentice-Hall, Englewood Cliffs, NJ, USA, 3rd edition, 1993.
  14. E. Lindström, J. Ströjby, M. Brodén, M. Wiktorsson, and J. Holst, “Sequential calibration of options,” Computational Statistics & Data Analysis, vol. 52, no. 6, pp. 2877–2891, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  15. O. E. Barndorff-Nielsen and N. Shephard, “Power and bipower variation with stochastic volatility and jumps,” Journal of Financial Econometrics, vol. 2, no. 1, pp. 1–37, 2004. View at Google Scholar
  16. T. Bollerslev, “Generalized autoregressive conditional heteroskedasticity,” Journal of Econometrics, vol. 31, no. 3, pp. 307–327, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  17. S.-H. Poon and C. W. J. Granger, “Forecasting volatility in financial markets: a review,” Journal of Economic Literature, vol. 41, no. 2, pp. 478–539, 2003. View at Publisher · View at Google Scholar · View at Scopus
  18. R. Cont, “Model uncertainty and its impact on the pricing of derivative instruments,” Mathematical Finance, vol. 16, no. 3, pp. 519–547, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. F. O. Bunnin, Y. Guo, and Y. Ren, “Option pricing under model and parameter uncertainty using predictive densities,” Statistics and Computing, vol. 12, no. 1, pp. 37–44, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  20. P. P. Boyle and A. L. Ananthanarayanan, “The impact of varince estimation in option valuation models,” Journal of Financial Economics, vol. 5, pp. 375–387, 1977. View at Google Scholar
  21. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Springer Series in Statistics, Springer, New York, NY, USA, 2001. View at MathSciNet
  22. D. Brigo, F. Mercurio, and F. Rapisarda, “Smile at the uncertainty,” Risk, vol. 17, no. 5, pp. 97–101, 2004. View at Google Scholar
  23. J. M. Harrison and S. R. Pliska, “Martingales and stochastic integrals in the theory of continuous trading,” Stochastic Processes and Their Applications, vol. 11, no. 3, pp. 215–260, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. S. Biagini and R. Cont, “Model-free representation of pricing rules as conditional expectations,” in Stochastic Processes and Applications to Mathematical Finance, J. Akahori, S. Ogawa, and S. Watanabe, Eds., pp. 53–66, World Scientific, 2006. View at Google Scholar
  25. T. G. Andersen, T. Bollerslev, F. X. Diebold, and P. Labys, “Modeling and forecasting realized volatility,” Econometrica, vol. 71, no. 2, pp. 579–625, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. D. Williams, Probability with Martingales, Cambridge Mathematical Textbooks, Cambridge University Press, Cambridge, UK, 1991. View at MathSciNet
  27. J. C. Hull and A. White, “The pricing of options on assets with stochastic volatility,” Journal of Finance, vol. 42, no. 2, pp. 281–300, 1987. View at Google Scholar
  28. S. Asmussen and J. Rosiński, “Approximations of small jumps of Lévy processes with a view towards simulation,” Journal of Applied Probability, vol. 38, no. 2, pp. 482–493, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. P. Cizeau, Y. Liu, M. Meyer, C.-K. Peng, and H. E. Stanley, “Volatility distribution in the S&P500 stock index,” Physica A, vol. 245, no. 3-4, pp. 441–445, 1997. View at Google Scholar · View at Scopus