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Une application de la formule de Jarrow et Rudd aux options sur indice CAC 40

Author

Listed:
  • Gunther Capelle-Blancard

    (TEAM - Théories et Applications en Microéconomie et Macroéconomie - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Emmanuel Jurczenko

    (TEAM - Théories et Applications en Microéconomie et Macroéconomie - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Many empirical studies pointed out that the Black-Scholes model led to a wrong evaluation of deep in-the-money options and deep out-the-money options. These biases are usually attributed to the hypothesis of log-normality of the underlying asset. In order to remove these biaises, Jarrow and Rudd (1982) propose to use a series expansion for the state price density. This approach allows to take non-normal skewness and kurtosis in asset returns into account. Using high frequency data from the SBF database, we examine the explicative and predictive performance of the Jarrow and Rudd option valuation. We find that Jarrow and Rudd's model improves the valuation of CAC 40 index option (PXL).

Suggested Citation

  • Gunther Capelle-Blancard & Emmanuel Jurczenko, 2000. "Une application de la formule de Jarrow et Rudd aux options sur indice CAC 40," Post-Print halshs-03723832, HAL.
  • Handle: RePEc:hal:journl:halshs-03723832
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03723832
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    References listed on IDEAS

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    1. Dilip B. Madan & Frank Milne, 1994. "Contingent Claims Valued And Hedged By Pricing And Investing In A Basis," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 223-245, July.
    2. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," The Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-752.
    3. Das, Sanjiv Ranjan & Sundaram, Rangarajan K., 1999. "Of Smiles and Smirks: A Term Structure Perspective," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(2), pages 211-239, June.
    4. Robert JARROW & Andrew RUDD, 2008. "Approximate Option Valuation For Arbitrary Stochastic Processes," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 1, pages 9-31, World Scientific Publishing Co. Pte. Ltd..
    5. Michael Rockinger & Eric Jondeau, 1997. "Estimation et interprétation des densités neutres au risque: une comparaison de méthodes," Working Papers hal-00601588, HAL.
    6. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    7. Charles J. Corrado & Tie Su, 1996. "S&P 500 index option tests of Jarrow and Rudd's approximate option valuation formula," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 16(6), pages 611-629, September.
    8. C. J. Corrado & Tie Su, 1997. "Implied volatility skews and stock return skewness and kurtosis implied by stock option prices," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 73-85, March.
    9. Campbell R. Harvey & Robert E. Whaley, 1992. "Dividends and S&P 100 index option valuation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 12(2), pages 123-137, April.
    10. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    11. Peter A. Abken & Dilip B. Madan & Buddhavarapu Sailesh Ramamurtie, 1996. "Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar futures options," FRB Atlanta Working Paper 96-5, Federal Reserve Bank of Atlanta.
    12. 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.
    13. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    14. Eric Renault & Nizar Touzi, 1996. "Option Hedging And Implied Volatilities In A Stochastic Volatility Model1," Mathematical Finance, Wiley Blackwell, vol. 6(3), pages 279-302, July.
    15. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    16. Hull, John C & White, Alan D, 1987. "The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
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    More about this item

    Keywords

    option pricing models; density probability functions; volatility forecast; Edgeworth expansion; modèles d'évaluation d'options; fonction de densité de probabilité; prévision de volatilité; développement d'Edgeworth;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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