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Probing Option Prices for Information

Author

Listed:
  • Hélyette Geman

    (University of London
    ESSEC)

  • Dilip B. Madan

    (University of Maryland)

  • Marc Yor

    (Université Paris VI)

Abstract

We present a methodology for extracting information from option prices when the market is viewed as knowledgeable. By expanding the information filtration judiciously and determining conditional characteristic functions for the log of the stock price, we obtain option pricing formulae which when fit to market data may reveal this information. In particular, we consider probing option prices for knowledge of the future stock price, instantaneous volatility, and the asymptotic dividend stream. Additionally the bridge laws developed are also useful for simulation based on stratified sampling that conditions on the terminal values of paths.

Suggested Citation

  • Hélyette Geman & Dilip B. Madan & Marc Yor, 2007. "Probing Option Prices for Information," Methodology and Computing in Applied Probability, Springer, vol. 9(1), pages 115-131, March.
    • Handle: RePEc:spr:metcap:v:9:y:2007:i:1:d:10.1007_s11009-006-9005-3
    DOI: 10.1007/s11009-006-9005-3
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    References listed on IDEAS

    as
    1. Peter Carr & Hélyette Geman & Dilip B. Madan & Marc Yor, 2003. "Stochastic Volatility for Lévy Processes," Mathematical Finance, Wiley Blackwell, vol. 13(3), pages 345-382, July.
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    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-681.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    8. Carr, Peter & Madan, Dilip B., 2005. "A note on sufficient conditions for no arbitrage," Finance Research Letters, Elsevier, vol. 2(3), pages 125-130, September.
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    11. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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    Cited by:

    1. Dorje C. Brody & Mark H. A. Davis & Robyn L. Friedman & Lane P. Hughston, 2008. "Informed Traders," Papers 0807.1253, arXiv.org, revised Nov 2008.
    2. Hoyle, Edward & Hughston, Lane P. & Macrina, Andrea, 2011. "Lévy random bridges and the modelling of financial information," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 856-884, April.

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