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Loss Functions in Option Valuation: A Framework for Selection

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Author Info

  • Dennis Bams

    ()
    (Department of Finance, Maastricht University, 6200 MD Maastricht, The Netherlands)

  • Thorsten Lehnert

    ()
    (Department of Finance, Maastricht University, 6200 MD Maastricht, The Netherlands)

  • Christian C. P. Wolff

    ()
    (Luxembourg School of Finance, University of Luxembourg, L-1246 Luxembourg)

Abstract

In this paper, we investigate the importance of different loss functions when estimating and evaluating option pricing models. Our analysis shows that it is important to take into account parameter uncertainty, because this leads to uncertainty in the predicted option price. We illustrate the effect on the out-of-sample pricing errors in an application of the ad hoc Black-Scholes model to DAX index options. We confirm the empirical results of Christoffersen and Jacobs (Christoffersen, P., K. Jacobs. 2004. The importance of the loss function in option valuation. J. Financial Econom. 72 291-318) and find strong evidence for their conjecture that the squared pricing error criterion may serve as a general-purpose loss function in option valuation applications. At the same time, we provide a first yardstick to evaluate the adequacy of the loss function. This is accomplished through a data-driven method to deliver not just a point estimate of the root mean squared pricing error, but a distribution.

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File URL: http://dx.doi.org/10.1287/mnsc.1080.0976
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 55 (2009)
Issue (Month): 5 (May)
Pages: 853-862

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Handle: RePEc:inm:ormnsc:v:55:y:2009:i:5:p:853-862

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Related research

Keywords: option pricing; loss functions; estimation risk; GARCH; implied volatility;

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Cited by:
  1. Bekkour, Lamia & Jin, Xisong & Lehnert, Thorsten & Rasmouki, Fanou & Wolff, Christian C, 2012. "Euro at Risk: The Impact of Member Countries’ Credit Risk on the Stability of the Common Currency," CEPR Discussion Papers 9229, C.E.P.R. Discussion Papers.
  2. Christian Wolff & Thorsten Lehnert & Cokki Versluis, 2009. "A Cumulative Prospect Theory Approach to Option Pricing," LSF Research Working Paper Series 09-03, Luxembourg School of Finance, University of Luxembourg.
  3. Kanniainen, Juho & Lin, Binghuan & Yang, Hanxue, 2014. "Estimating and using GARCH models with VIX data for option valuation," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 200-211.
  4. Frijns, Bart & Lehnert, Thorsten & Zwinkels, Remco C.J., 2011. "Modeling structural changes in the volatility process," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 522-532, June.
  5. Ryszard Kokoszczyński & Natalia Nehrebecka & Paweł Sakowski & Paweł Strawiński & Robert Ślepaczuk, 2010. "Option Pricing Models with HF Data – a Comparative Study. The Properties of Black Model with Different Volatility Measures," Working Papers 2010-03, Faculty of Economic Sciences, University of Warsaw.

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