Model uncertainty and its impact on the pricing of derivative instruments
AbstractModel 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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Bibliographic InfoPaper provided by HAL in its series Post-Print with number halshs-00002695.
Date of creation: 2006
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Publication status: Published, Mathematical Finance, 2006, 16, 3, 519 - 547
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decision under ambiguity; uncertainty; option pricing; risk measures; mathematical finance;
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- M. Avellaneda & A. Levy & A. ParAS, 1995. "Pricing and hedging derivative securities in markets with uncertain volatilities," Applied Mathematical Finance, Taylor and Francis Journals, vol. 2(2), pages 73-88.
- Adam, Klaus, 2003.
"On the Relation between Robust and Bayesian Decision Making,"
CFS Working Paper Series
2003/02, Center for Financial Studies (CFS).
- Adam, Klaus, 2004. "On the relation between robust and Bayesian decision making," Journal of Economic Dynamics and Control, Elsevier, vol. 28(10), pages 2105-2117, September.
- 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.
- 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).
- Zengjing Chen & Larry Epstein, 2002. "Ambiguity, Risk, and Asset Returns in Continuous Time," Econometrica, Econometric Society, vol. 70(4), pages 1403-1443, July.
- Marco Avellaneda & Antonio ParAS, 1996. "Managing the volatility risk of portfolios of derivative securities: the Lagrangian uncertain volatility model," Applied Mathematical Finance, Taylor and Francis Journals, vol. 3(1), pages 21-52.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Christophe Boucher & Benjamin Hamidi & Patrick Kouontchou & Bertrand Maillet, 2012.
"Une évaluation économique du risque de modèle pour les investisseurs de long terme,"
Presses de Sciences-Po, vol. 63(3), pages 591-600.
- Christophe Boucher & Benjamin Hamidi & Patrick Kouontchou & Bertrand Maillet, 2012. "Une Evaluation Economique du risque de modèle pour les investisseurs de long-terme," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00825337, HAL.
- repec:hal:journl:halshs-00587779 is not listed on IDEAS
- Jakob Söhl, 2012. "Confidence sets in nonparametric calibration of exponential Lévy models," SFB 649 Discussion Papers SFB649DP2012-012, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Jakob S\"ohl & Mathias Trabs, 2012. "Option calibration of exponential L\'evy models: Confidence intervals and empirical results," Papers 1202.5983, arXiv.org, revised Oct 2012.
- Jacob Söhl & Mathias Trabs, 2012. "Option calibration of exponential Lévy models: Implementation and empirical results," SFB 649 Discussion Papers SFB649DP2012-017, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
- Kerkhof, Jeroen & Melenberg, Bertrand & Schumacher, Hans, 2010. "Model risk and capital reserves," Journal of Banking & Finance, Elsevier, vol. 34(1), pages 267-279, January.
- Alexander Schied, 2013. "Model-free CPPI," Papers 1305.5915, arXiv.org, revised Jul 2013.
- Larry G. Epstein & Shaolin Ji, 2013.
"Ambiguous volatility and asset pricing in continuous time,"
- Larry G. Epstein & Shaolin Ji, 2013. "Ambiguous Volatility and Asset Pricing in Continuous Time," Review of Financial Studies, Society for Financial Studies, vol. 26(7), pages 1740-1786.
- Larry G. Epstein & Shaolin Ji, 2012. "Ambiguous Volatility and Asset Pricing in Continuous Time," CIRANO Working Papers 2012s-29, CIRANO.
- Paolo Foschi & Andrea Pascucci, 2008.
"Path dependent volatility,"
Decisions in Economics and Finance,
Springer, vol. 31(1), pages 13-32, May.
- Pelsser, A. & Stadje, M.A., 2012. "Time-Consistent and Market-Consistent Evaluations (Revised version of CentER DP 2011-063)," Discussion Paper 2012-086, Tilburg University, Center for Economic Research.
- Jakob S\"ohl, 2012. "Confidence sets in nonparametric calibration of exponential L\'evy models," Papers 1202.6611, arXiv.org, revised Sep 2013.
- Alexander Cox & Jan Obłój, 2011. "Robust pricing and hedging of double no-touch options," Finance and Stochastics, Springer, vol. 15(3), pages 573-605, September.
- Thomas Breuer & Imre Csiszar, 2013. "Measuring Model Risk," Papers 1301.4832, arXiv.org.
- Marcel Nutz, 2013. "Utility Maximization under Model Uncertainty in Discrete Time," Papers 1307.3597, arXiv.org.
- Florence Guillaume & Wim Schoutens, 2012. "Calibration risk: Illustrating the impact of calibration risk under the Heston model," Review of Derivatives Research, Springer, vol. 15(1), pages 57-79, April.
- Zhang, Xin & Siu, Tak Kuen, 2009. "Optimal investment and reinsurance of an insurer with model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 81-88, August.
- Alexander, Carol & Nogueira, Leonardo M., 2007. "Model-free hedge ratios and scale-invariant models," Journal of Banking & Finance, Elsevier, vol. 31(6), pages 1839-1861, June.
- Johannes Siven & Rolf Poulsen, 2009. "Auto-static for the people: risk-minimizing hedges of barrier options," Review of Derivatives Research, Springer, vol. 12(3), pages 193-211, October.
- Fig-Talamanca, Gianna, 2009. "Testing volatility autocorrelation in the constant elasticity of variance stochastic volatility model," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2201-2218, April.
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