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Loss Functions in Option Valuation: A Framework for Model Selection

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Author Info
Bams, Dennis
Lehnert, Thorsten
Wolff, Christian C

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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, since 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. Our empirical results suggest that different loss functions lead to uncertainty about the pricing error itself. At the same time, it provides 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 pricing error, but a confidence interval.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 4960.

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Date of creation: Mar 2005
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Handle: RePEc:cpr:ceprdp:4960

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

Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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  1. 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. [Downloadable!] (restricted)
  2. 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. [Downloadable!] (restricted)
  3. Hutchinson, James M & Lo, Andrew W & Poggio, Tomaso, 1994. " A Nonparametric Approach to Pricing and Hedging Derivative Securities via Learning Networks," Journal of Finance, American Finance Association, vol. 49(3), pages 851-89, July. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Peter Christoffersen & Kris Jacobs, 2003. "The Importance of the Loss Function in Option Valuation," CIRANO Working Papers 2003s-52, CIRANO. [Downloadable!]
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  6. Heston, Steven L & Nandi, Saikat, 2000. "A Closed-Form GARCH Option Valuation Model," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 13(3), pages 585-625.
  7. Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C, 2002. "An Evaluation Framework for Alternative VaR Models," CEPR Discussion Papers 3403, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  8. 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. [Downloadable!] (restricted)
  9. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO. [Downloadable!]
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