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Recovering Probabilistic Information From Options Prices and the Underlying

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  • Bruce Mizrach

    () (Rutgers University)

Abstract

This paper examines a variety of methods for extracting implied probability distributions from option prices and the underlying. The paper first explores non-parametric procedures for reconstructing densities directly from options market data. I then consider local volatility functions, both through implied volatility trees and volatility interpolation. I then turn to alternative specifications of the stochastic process for the underlying. I estimate a mixture of log normals model, apply it to exchange rate data, and illustrate how to conduct forecast comparisons. I finally turn to the estimation of jump risk by extracting bipower variation.

Suggested Citation

  • Bruce Mizrach, 2007. "Recovering Probabilistic Information From Options Prices and the Underlying," Departmental Working Papers 200702, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:200702
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    File URL: http://www.sas.rutgers.edu/virtual/snde/wp/2007-02.pdf
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    References listed on IDEAS

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    1. Haas, Markus & Mittnik, Stefan & Mizrach, Bruce, 2006. "Assessing central bank credibility during the ERM crises: Comparing option and spot market-based forecasts," Journal of Financial Stability, Elsevier, vol. 2(1), pages 28-54, April.
    2. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    3. Bjerksund, Petter & Stensland, Gunnar, 1993. "Closed-form approximation of American options," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages 87-99.
    4. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    5. Mizrach, Bruce, 1995. "Target zone models with stochastic realignments: an econometric evaluation," Journal of International Money and Finance, Elsevier, vol. 14(5), pages 641-657, October.
    6. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    7. Ritchey, Robert J, 1990. "Call Option Valuation for Discrete Normal Mixtures," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 13(4), pages 285-296, Winter.
    8. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    9. Robert Tompkins, 2001. "Implied volatility surfaces: uncovering regularities for options on financial futures," The European Journal of Finance, Taylor & Francis Journals, vol. 7(3), pages 198-230.
    10. Wiggins, James B., 1987. "Option values under stochastic volatility: Theory and empirical estimates," Journal of Financial Economics, Elsevier, vol. 19(2), pages 351-372, December.
    11. Skouras, Spyros, 2007. "Decisionmetrics: A decision-based approach to econometric modelling," Journal of Econometrics, Elsevier, vol. 137(2), pages 414-440, April.
    12. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
    13. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
    14. Bruce Mizrach, 2006. "The Enron Bankruptcy: When did the options market in Enron lose it’s smirk?," Review of Quantitative Finance and Accounting, Springer, vol. 27(4), pages 365-382, December.
    15. Bliss, Robert R. & Panigirtzoglou, Nikolaos, 2002. "Testing the stability of implied probability density functions," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 381-422, March.
    16. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-320, June.
    17. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
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    More about this item

    Keywords

    options; implied probability densities; volatility smile; jump risk; bipower variation;

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • F31 - International Economics - - International Finance - - - Foreign Exchange

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