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The Importance of the Loss Function in Option Pricing

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  • Peter Christoffersen

    ()

  • Kris Jacobs

    ()

Abstract

Which loss function should be used when estimating and evaluating option pricing models? Many different fucntions have been suggested, but no standard has emerged. We do not promote a partidular function, but instead emphasize that consistency in the choice of loss functions is crucial. First, for any given model, the loss function used in parameter estimation and model evaluation should be identical, otherwise suboptimal parameter estimates will be obtained. Second, when comparing models, the estimation loss function should be identical across models, otherwise unfair comparisons will be made. We illustrate the importance of these issues in an application of the so-called Practitioner Black-Scholes (PBS) model to S&P500 index options. We find reductions of over 50 percent in the root mean squared error of the PBS model when the estimation and evaluation loss functions are aligned. We also find that the PBS model outperforms a benchmark structural model when the estimation loss functions are identical across models, but otherwise not. The new PBS model with aligned loss functions thus represents a much tougher benchmark against which future structural models can be compared. Quelle fonction de pertes devrait être utilisée pour l'estimation et l'évaluation des modèles d'évaluation d'options? Plusieurs fonctions différentes ont été suggérées,0501s aucune norme ne s'est imposée. Nous ne promouvons aucune fonction,0501s soutenons que la cohérence dans le choix des fonctions est cruciale. Premièrement, pour n'importe quel modèle donné, la fonction de pertes utilisée dans l'estimation des paramètres et dans l'évaluation du modèle devrait être la même, sinon on obtient des estimations de paramètres sous-optimales. Deuxièmement, lors de la comparaison de modèles, la fonction de pertes pour l'estimation devrait être la même pour chaque modèle, autrement les comparaisons sont injustes. Nous illustrons l'importance de ces questions dans une application du modèle appelé Black-Scholes du praticien (PBS) aux options de l'index S&P500. Nous trouvons des réductions de plus de 50 pourcent de la racine de l'erreur quadratique moyenne du modèle PBS lorsque les fonctions de pertes d'estimation et d'évaluation sont alignées. Nous trouvons également que le modèle PBS dépasse un modèle de benchmark structurel quand les fonctions de pertes d'estimation sont identiques pour tous les modèles,0501s pas dans les autres cas. Le nouveau modèle PBS à fonctions de pertes alignées représente dès lors un benchmark bien plus robuste auquel les futurs modèles structurels pourront être comparés.

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Bibliographic Info

Paper provided by CIRANO in its series CIRANO Working Papers with number 2001s-45.

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Date of creation: 01 Jul 2001
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Handle: RePEc:cir:cirwor:2001s-45

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Keywords: Option pricing; implied volatility; practitioner Black-Scholes approach; pricing errors; loss functions; out-of-sample forecasting; parameter stability; Évaluation des options; volatilité implicite; approche Black-Scholes du praticien; erreurs d'évaluation; fonctions de perte; prévisions hors-échantillon; stabilité des paramètres;

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References

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  1. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
  2. Hausman, Jerry A, 1978. "Specification Tests in Econometrics," Econometrica, Econometric Society, vol. 46(6), pages 1251-71, November.
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Cited by:
  1. Haas, Markus & Mittnik, Stefan & Mizrach, Bruce, 2005. "Assessing central bank credibility during the EMS crises: Comparing option and spot market-based forecasts," CFS Working Paper Series 2005/09, Center for Financial Studies (CFS).
  2. René Garcia & Richard Luger & Éric Renault, 2001. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables (Note : New version February 2002) / Empirical Assessment of an Intertemporal Option Pricing Model with Latent Varia," CIRANO Working Papers 2001s-02, CIRANO.
  3. Ait-Sahalia, Yacine & Duarte, Jefferson, 2003. "Nonparametric option pricing under shape restrictions," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 9-47.
  4. Garcia, Rene & Luger, Richard & Renault, Eric, 2003. "Empirical assessment of an intertemporal option pricing model with latent variables," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 49-83.
  5. Peter Christoffersen & Kris Jacobs, 2002. "Which Volatility Model for Option Valuation?," CIRANO Working Papers 2002s-33, CIRANO.
  6. Bruce Mizrach, 2002. "When Did The Smart Money in Enron Lose Its' Smirk?," Departmental Working Papers 200224, Rutgers University, Department of Economics.
  7. Bates, David S., 2003. "Empirical option pricing: a retrospection," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 387-404.
  8. Bruce Mizrach, 2006. "The Enron Bankruptcy: When did the options market in Enron lose it’s smirk?," Review of Quantitative Finance and Accounting, Springer, vol. 27(4), pages 365-382, December.

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