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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.

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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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  1. 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 637-54, May-June.
  2. 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.
  3. James M. Hutchinson & Andrew W. Lo & Tomaso Poggio, 1994. "A Nonparametric Approach to Pricing and Hedging Derivative Securities Via Learning Networks," NBER Working Papers 4718, National Bureau of Economic Research, Inc.
  4. Bakshi, Gurdip & Cao, Charles & Chen, Zhiwu, 1997. " Empirical Performance of Alternative Option Pricing Models," Journal of Finance, American Finance Association, vol. 52(5), pages 2003-49, December.
  5. Peter Christoffersen & Kris Jacobs, 2003. "The Importance of the Loss Function in Option Valuation," CIRANO Working Papers 2003s-52, CIRANO.
  6. 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.
  7. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
  8. 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, 06.
  9. 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.
  10. 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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