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Model uncertainty and its impact on the pricing of derivative instruments

  • Rama Cont


    (CMAP - Centre de Mathématiques Appliquées - CNRS - UVSQ - Université de Versailles Saint-Quentin-en-Yvelines - Polytechnique - X)

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    Model uncertainty, in the context of derivative pricing, can be defined as the uncertainty on the value of a contingent claim resulting from the lack of precise knowledge of the pricing model to be used for its valuation. We introduce here a quantitative framework for defining model uncertainty in option pricing models. After discussing some properties which a quantitative measure of model uncertainty should verify in order to be useful and relevant in the context of risk measurement and management, we propose a method for measuring model uncertainty which verifies these properties and yields numbers which are comparable to other risk measures and compatible with observations of market prices of a set of benchmark derivatives. We illustrate the difference between model uncertainty and the more common notion of "market risk" through examples. Finally, we illustrate the connection between our proposed measure of model uncertainty and the recent literature on coherent and convex risk measures.

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    Paper provided by HAL in its series Post-Print with number halshs-00002695.

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    Date of creation: 2006
    Date of revision:
    Publication status: Published in Mathematical Finance, Wiley, 2006, 16 (3), pp.519 - 547. <10.1111/j.1467-9965.2006.00281.x>
    Handle: RePEc:hal:journl:halshs-00002695
    DOI: 10.1111/j.1467-9965.2006.00281.x
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    1. M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(2), pages 73-88.
    2. Zengjing Chen & Larry G. Epstein, 2000. "Ambiguity, risk and asset returns in continuous time," RCER Working Papers 474, University of Rochester - Center for Economic Research (RCER).
    3. Klaus Adam, 2001. "On the Relation between Robust and Bayesian Decision Making," CSEF Working Papers 68, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    4. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    5. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    6. Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(1), pages 21-52.
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