Specification Tests of Calibrated Option Pricing Models
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 diÂ¤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 diÂ¢ 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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