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Option prices as probabilities

Author

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

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.

Suggested Citation

  • Madan, D. & Roynette, B. & Yor, Marc, 2008. "Option prices as probabilities," Finance Research Letters, Elsevier, vol. 5(2), pages 79-87, June.
    • Handle: RePEc:eee:finlet:v:5:y:2008:i:2:p:79-87
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    References listed on IDEAS

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    1. 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..
    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 621-651, October.
    4. 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.
    5. 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.
    6. repec:dau:papers:123456789/1448 is not listed on IDEAS
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    Cited by:

    1. Lingjiong Zhu, 2015. "Short maturity options for Azéma–Yor martingales," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(04), pages 1-32, December.
    2. Konstantinos Konstantaras & Vasilios Sogiakas, 2019. "Is stock liquidity transferred and upgraded in acquisitions? Evidence from liquidity synergies in US freeze-outs," Annals of Operations Research, Springer, vol. 282(1), pages 179-216, November.
    3. Ashkan Nikeghbali & Eckhard Platen, 2008. "On honest times in financial modeling," Papers 0808.2892, arXiv.org.
    4. 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.
    5. Baurdoux, Erik J. & Pedraza, José M., 2023. "Predicting the last zero before an exponential time of a spectrally negative Lévy process," LSE Research Online Documents on Economics 119290, London School of Economics and Political Science, LSE Library.
    6. D. Madan & B. Roynette & M. Yor, 2008. "Unifying Black–Scholes Type Formulae Which Involve Brownian Last Passage Times up to a Finite Horizon," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(2), pages 97-115, June.
    7. 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.
    8. 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.
    9. Libo Li, 2018. "Characterisation of honest times and optional semimartingales of class-($\Sigma$)," Papers 1801.03873, arXiv.org, revised Dec 2021.
    10. Libo Li, 2022. "Characterisation of Honest Times and Optional Semimartingales of Class- $$(\Sigma )$$ ( Σ )," Journal of Theoretical Probability, Springer, vol. 35(4), pages 2145-2175, December.

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