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Loss Functions in Option Valuation: A Framework for Model Selection

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  • Bams, Dennis
  • Lehnert, Thorsten
  • Wolff, Christian C

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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Bibliographic Info

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

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  1. 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.
  2. 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.
  3. 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.
  4. 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.
  5. Jin-Chuan Duan & Jean-Guy Simonato, 1995. "Empirical Martingale Simulation for Asset Prices," CIRANO Working Papers 95s-43, CIRANO.
  6. 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.
  7. 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.
  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. 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.
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Cited by:
  1. Thorsten Lehnert & Bart Frijns & Remco Zwinkels, 2009. "A Volatility Targeting GARCH model with Time-Varying Coefficients," LSF Research Working Paper Series 09-08, Luxembourg School of Finance, University of Luxembourg.
  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.

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