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Building a Consistent Pricing Model from Observed Option Prices

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  • Laurent, Jean-Paul
  • Dietmar P.J. Leisen
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    Abstract

    This paper constructs a model for the evolution of a risky security that is consistent with a set of observed call option prices. It explicitly treats the fact that only a discrete data set can be observed in practice. The framework is general and allows for state dependent volatility and jumps. The theoretical properties are studied. An easy procedure to check for arbitrage opportunities in market data is proved and then used to ensure the feasibility of our approach. The implementation is discussed: testing on market data reveals a U-shaped form for the "local volatility" depending on the state and, surprisingly, a large probability for strong price movements.

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    File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonsfb/bonsfb443.pdf
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    Bibliographic Info

    Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 443.

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    Length: pages
    Date of creation: Dec 1998
    Date of revision:
    Handle: RePEc:bon:bonsfb:443

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    Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
    Fax: +49 228 73 6884
    Web page: http://www.bgse.uni-bonn.de

    Related research

    Keywords: Markov Chain; no-arbitrage; cross-entropy; model risk;

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    References

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    1. Buchen, Peter W. & Kelly, Michael, 1996. "The Maximum Entropy Distribution of an Asset Inferred from Option Prices," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(01), pages 143-159, March.
    2. Lars Peter Hansen & Ravi Jagannathan, 1994. "Assessing specification errors in stochastic discount factor models," Staff Report 167, Federal Reserve Bank of Minneapolis.
    3. Luttmer, Erzo G J, 1996. "Asset Pricing in Economies with Frictions," Econometrica, Econometric Society, vol. 64(6), pages 1439-67, November.
    4. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    5. Jackwerth, Jens Carsten & Rubinstein, Mark, 1996. " Recovering Probability Distributions from Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1611-32, December.
    6. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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    Cited by:
    1. Cousot, Laurent, 2007. "Conditions on option prices for absence of arbitrage and exact calibration," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3377-3397, November.

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