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Option prices as probabilities

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  • Madan, D.
  • Roynette, B.
  • Yor, Marc
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    Abstract

    Four distribution functions are associated with call and put prices seen as functions of their strike and maturity. The random variables associated with these distributions are identified when the process for moneyness defined as the stock price relative to the forward price is a positive local martingale with no positive jumps that tends to zero at infinity. Results on calls require moneyness to be a continuous martingale as well. It is shown that for puts the distributions in the strike are those for the remaining supremum while for calls, they relate to the remaining infimum. In maturity we see the distribution functions for the last passage times of moneyness to strike.

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    Bibliographic Info

    Article provided by Elsevier in its journal Finance Research Letters.

    Volume (Year): 5 (2008)
    Issue (Month): 2 (June)
    Pages: 79-87

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    Handle: RePEc:eee:finlet:v:5:y:2008:i:2:p:79-87

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    Web page: http://www.elsevier.com/locate/frl

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    References

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    1. 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 637-54, May-June.
    2. Peter Carr & Helyette Geman & Dilip Madan & Marc Yor, 2004. "From local volatility to local Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 4(5), pages 581-588.
    3. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-51, October.
    4. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    5. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
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    Cited by:
    1. Ashkan Nikeghbali & Eckhard Platen, 2008. "On honest times in financial modeling," Papers 0808.2892, arXiv.org.
    2. D. Madan & B. Roynette & M. Yor, 2008. "Unifying BlackÔÇôScholes Type Formulae Which Involve Brownian Last Passage Times up to a Finite Horizon," Asia-Pacific Financial Markets, Springer, vol. 15(2), pages 97-115, June.
    3. Ashkan Nikeghbali & Eckhard Platen, 2013. "A reading guide for last passage times with financial applications in view," Finance and Stochastics, Springer, vol. 17(3), pages 615-640, July.
    4. Yuri Imamura, 2011. "A remark on static hedging of options written on the last exit time," Review of Derivatives Research, Springer, vol. 14(3), pages 333-347, October.
    5. Amel Bentata & Marc Yor, 2008. "From Black-Scholes and Dupire formulae to last passage times of local martingales. Part A : The infinite time horizon," Papers 0806.0239, arXiv.org.

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