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Specification Tests of Calibrated Option Pricing Models

  • Jarrow, Robert
  • Kwok, Simon

In spite of the popularity of model calibration in finance, empirical researchers have put more emphasis on model estimation than on the equally important goodness-of-fit problem.This is due partly to the ignorance of modelers, and more to the ability of existing statistical tests to detect specification errors. In practice, models are often calibrated by minimizing a loss function of the differences between the modelled and actual observations. Under this approach, it is challenging to disentangle model error from estimation error in the residual series. To circumvent the difficulty, we study an alternative way of estimating the model by exact calibration. Unlike the error minimization approach, all information about dynamic misspecifications is channeled to the parameter estimation residuals under exact calibration.In the context of option pricing, we illustrate that standard time series tests are powerful in detecting various kinds of dynamic misspecifications. Compared to the error minimization approach, exact calibration yields more reasonable model comparison result, and delivers more accurate hedging performance that is robust to both gradual and abrupt structural shifts of state 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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Date of creation: May 2013
Date of revision: Dec 2014
Handle: RePEc:syd:wpaper:2123/9191
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  1. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  2. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2015. "Parametric Inference and Dynamic State Recovery From Option Panels," Econometrica, Econometric Society, vol. 83(3), pages 1081-1145, 05.
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  13. 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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  16. Merton, Robert C, 1976. "The Impact on Option Pricing of Specification Error in the Underlying Stock Price Returns," Journal of Finance, American Finance Association, vol. 31(2), pages 333-50, May.
  17. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-43.
  18. 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.
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