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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.

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File URL: ftp://snde.rutgers.edu/Rutgers/wp/2007-02.pdf
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Bibliographic Info

Paper provided by Rutgers University, Department of Economics in its series Departmental Working Papers with number 200702.

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Length: 20 pages
Date of creation: 19 Jan 2007
Date of revision:
Publication status: forthcoming in Cheng-few Lee and Alice C. Lee (eds.), Handbook of Quantitative Finance
Handle: RePEc:rut:rutres:200702

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

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References

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  1. Barone-Adesi, Giovanni & Whaley, Robert E, 1987. " Efficient Analytic Approximation of American Option Values," Journal of Finance, American Finance Association, vol. 42(2), pages 301-20, June.
  2. 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.
  3. 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.
  4. Peter Christoffersen & Kris Jacobs, 2003. "The Importance of the Loss Function in Option Valuation," CIRANO Working Papers 2003s-52, CIRANO.
  5. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Papers 2003-W21, Economics Group, Nuffield College, University of Oxford.
  6. 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 285-96, Winter.
  7. Peter Carr & Liuren Wu, 2002. "Time-Changed Levy Processes and Option Pricing," Finance 0207011, EconWPA.
  8. 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 841-62, November.
  9. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
  10. Bjerksund, Petter & Stensland, Gunnar, 1993. "Closed-form approximation of American options," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages S87-S99.
  11. Spyros Skouras, 2001. "Decisionmetrics: A Decision-Based Approach to Econometric Modeling," Working Papers 01-11-064, Santa Fe Institute.
  12. 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.
  13. 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.
  14. 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.
  15. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  16. 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.
  17. 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 727-52.
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