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Specification Tests of Calibrated Option Pricing Models

  • Jarrow, Robert
  • Kwok, Simon

In spite of the popularity of model calibration in .nance, empirical researchers have putmore emphasis on model estimation than on the equally important goodness-of-.t problem.This is due partly to the ignorance of modelers, and more to the ability of existing statisticaltests to detect speci.cation errors. In practice, models are often calibrated by minimizinga loss function of the di¤erences between the modelled and actual observations. Under thisapproach, it is challenging to disentangle model error from estimation error in the residualseries. To circumvent the di¢ culty, we study an alternative way of estimating the model byexact calibration. Unlike the error minimization approach, all information about dynamicmisspeci.cations is channeled to the parameter estimation residuals under exact calibration.In the context of option pricing, we illustrate that standard time series tests are powerfulin detecting various kinds of dynamic misspeci.cations. Compared to the error minimizationapproach, exact calibration yields more reasonable model comparison result, and delivers moreaccurate hedging performance that is robust to both gradual and abrupt structural shifts ofstate variables.

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Paper provided by University of Sydney, School of Economics in its series Working Papers with number 2013-08.

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Handle: RePEc:syd:wpaper:2123/9191
Contact details of provider: Postal: Sydney, NSW 2006
Phone: 61 +2 9351 5055
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Web page: http://sydney.edu.au/arts/economics
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  1. Bates, David S., 2000. "Post-'87 crash fears in the S&P 500 futures option market," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 181-238.
  2. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
  3. 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.
  4. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-33, March.
  5. Hong, Yongmiao & Lee, Yoon-Jin, 2007. "An Improved Generalized Spectral Test For Conditional Mean Models In Time Series With Conditional Heteroskedasticity Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 23(01), pages 106-154, February.
  6. Pan, Jun, 2002. "The jump-risk premia implicit in options: evidence from an integrated time-series study," Journal of Financial Economics, Elsevier, vol. 63(1), pages 3-50, January.
  7. Yongmiao Hong & Yoon-Jin Lee, 2005. "Generalized Spectral Tests for Conditional Mean Models in Time Series with Conditional Heteroscedasticity of Unknown Form," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 499-541.
  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.
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