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The Importance of the Loss Function in Option Valuation

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Author Info
Peter Christoffersen ()
Kris Jacobs ()

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Abstract

Which loss function should be used when estimating and evaluating option valuation models? Many different functions have been suggested, but no standard has emerged. We 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 the same, otherwise suboptimal parameter estimates may be obtained. Second, when comparing models, the estimation loss function should be identical across models, otherwise inappropriate comparisons will be made. We illustrate the importance of these issues in an application of the so-called Practitioner Black-Scholes model to S&P 500 index options.

Quelle devrait être la fonction de perte utilisée pour l'estimation et l'évaluation des modèles de valorisation des options? Plusieurs fonctions ont été suggérées, mais aucune norme ne s'est imposée. Dans ce travail, nous ne proposons pas une fonction en particulier, mais nous soutenons que la cohérence dans le choix des fonctions est cruciale. Premièrement, pour n'importe quel modèle donné, la fonction de perte utilisée dans l'estimation des paramètres et dans l'évaluation du modèle devrait être la même, sinon on obtient des estimations de paramètres sous-optimaux. Deuxièmement, lors de la comparaison des modèles, la fonction de perte utilisée 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'indice S&P500.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2003s-52.

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Date of creation: 01 Aug 2003
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Handle: RePEc:cir:cirwor:2003s-52

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Related research
Keywords: implied volatility functions valuation errors out-of-sample forecasting parameter stability fonctions de volatilité implicite évaluation des erreurs prévision hors échantillon stabilité des paramètres

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Find related papers by JEL classification:
G12 - Financial Economics - - General Financial Markets - - - Asset Pricing
G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Melino, Angelo & Turnbull, Stuart M., 1990. "Pricing foreign currency options with stochastic volatility," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 239-265. [Downloadable!] (restricted)
  2. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(1), pages 69-107. [Downloadable!] (restricted)
  3. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June. [Downloadable!] (restricted)
  4. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, 06. [Downloadable!] (restricted)
  5. Garcia, R. & Luger, R. & Renault, E., 2000. "Empirical Assessment of an Intertemporal Option Pricing Model with Latent Variables," Papers 2000-56, Institut National de la Statistique et des Etudes Economiques-.
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  6. Brandt, Michael W. & Wu, Tao, 2002. "Cross-sectional tests of deterministic volatility functions," Journal of Empirical Finance, Elsevier, vol. 9(5), pages 525-550, December. [Downloadable!] (restricted)
  7. Jacquier, Eric & Jarrow, Robert, 2000. "Bayesian analysis of contingent claim model error," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 145-180. [Downloadable!] (restricted)
  8. 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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  9. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  10. Garcia, Rene & Gencay, Ramazan, 2000. "Pricing and hedging derivative securities with neural networks and a homogeneity hint," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 93-115. [Downloadable!] (restricted)
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  11. 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)
  12. 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)
  13. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 6(2), pages 327-43. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Bams, Dennis & Lehnert, Thorsten & Wolff, Christian C, 2005. "Loss Functions in Option Valuation: A Framework for Model Selection," CEPR Discussion Papers 4960, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  2. Dennis Kristensen & Anders Rahbek, 2007. "Likelihood-Based Inference in Nonlinear Error-Correction Models," CREATES Research Papers 2007-38, School of Economics and Management, University of Aarhus. [Downloadable!]
  3. Allan Timmermann & Andrew J. Patton, 2004. "Properties of Optimal Forecasts," Econometric Society 2004 North American Winter Meetings 234, Econometric Society. [Downloadable!]
    Other versions:
  4. Bruce Mizrach, 2007. "Recovering Probabilistic Information From Options Prices and the Underlying," Departmental Working Papers 200702, Rutgers University, Department of Economics. [Downloadable!]
  5. Andrew J. Patton & Kevin Sheppard, 2008. "Evaluating Volatility and Correlation Forecasts," OFRC Working Papers Series 2008fe22, Oxford Financial Research Centre. [Downloadable!]
  6. Silvia Goncalves & Massimo Guidolin, 2005. "Predictable dynamics in the S&P 500 index options implied volatility surface," Working Papers 2005-010, Federal Reserve Bank of St. Louis. [Downloadable!]
    Other versions:
  7. Elliott, Graham & Timmermann, Allan G, 2007. "Economic Forecasting," CEPR Discussion Papers 6158, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  8. Andrew Patton, 2006. "Volatility Forecast Comparison using Imperfect Volatility Proxies," Research Paper Series 175, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  9. Sadayuki Ono, 2007. "Option Pricing under Stochastic Volatility and Trading Volume," Discussion Papers 07/05, Department of Economics, University of York. [Downloadable!]
  10. Peter Christoffersen & Kris Jacobs & Gregory Vainberg, 2007. "Forward-Looking Betas," CREATES Research Papers 2007-39, School of Economics and Management, University of Aarhus. [Downloadable!]
  11. Peter Christoffersen & Kris Jacobs & Karim Mimouni, 2007. "Models for S&P500 Dynamics: Evidence from Realized Volatility, Daily Returns, and Option Prices," CREATES Research Papers 2007-37, School of Economics and Management, University of Aarhus. [Downloadable!]
  12. Stanislav Anatolyev, 2006. "Dynamic modeling under linear-exponential loss," Working Papers w0092, Center for Economic and Financial Research (CEFIR). [Downloadable!]
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