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Loss Functions in Option Valuation: A Framework for Selection


  • 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)


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.

Suggested Citation

  • Dennis Bams & Thorsten Lehnert & Christian C. P. Wolff, 2009. "Loss Functions in Option Valuation: A Framework for Selection," Management Science, INFORMS, vol. 55(5), pages 853-862, May.
  • Handle: RePEc:inm:ormnsc:v:55:y:2009:i:5:p:853-862

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    References listed on IDEAS

    1. Allen M. Poteshman, 2001. "Underreaction, Overreaction, and Increasing Misreaction to Information in the Options Market," Journal of Finance, American Finance Association, vol. 56(3), pages 851-876, June.
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    4. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
    5. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
    6. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Society for Financial Studies, vol. 13(3), pages 585-625.
    7. Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C.P., 2005. "An evaluation framework for alternative VaR-models," Journal of International Money and Finance, Elsevier, vol. 24(6), pages 944-958, October.
    8. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    9. 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.
    10. Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1998. "Implied Volatility Functions: Empirical Tests," Journal of Finance, American Finance Association, vol. 53(6), pages 2059-2106, December.
    11. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
    12. Blair, Bevan J. & Poon, Ser-Huang & Taylor, Stephen J., 2001. "Forecasting S&P 100 volatility: the incremental information content of implied volatilities and high-frequency index returns," Journal of Econometrics, Elsevier, vol. 105(1), pages 5-26, November.
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    Cited by:

    1. Bekkour, Lamia & Jin, Xisong & Lehnert, Thorsten & Rasmouki, Fanou & Wolff, Christian, 2015. "Euro at risk: The impact of member countries' credit risk on the stability of the common currency," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 67-83.
    2. 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.
    3. Thorsten Lehnert & Gildas Blanchard & Dennis Bams, 2014. "Evaluating Option Pricing Model Performance Using Model Uncertainty," LSF Research Working Paper Series 14-06, Luxembourg School of Finance, University of Luxembourg.
    4. 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.
    5. 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.
    6. 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.

    More about this item


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

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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