Specification Tests of Calibrated Option Pricing Models

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 modeled 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.

[1]  W. Härdle,et al.  Calibration Risk for Exotic Options , 2006 .

[2]  S. Heston,et al.  A Closed-Form GARCH Option Valuation Model , 2000 .

[3]  A. Lo,et al.  Nonparametric Estimation of State‐Price Densities Implicit in Financial Asset Prices , 1998 .

[4]  Jun Pan The jump-risk premia implicit in options: evidence from an integrated time-series study $ , 2002 .

[5]  M. Pesaran,et al.  TESTING NON-NESTED NONLINEAR REGRESSION MODELS , 1978 .

[6]  Peter Christoffersen,et al.  Série Scientifique Scientific Series the Importance of the Loss Function in Option Valuation the Importance of the Loss Function in Option Valuation , 2022 .

[7]  Jun Pan The Jump-Risk Premia Implicit in Options : Evidence from an Integrated Time-Series Study , 2001 .

[8]  Gurdip Bakshi,et al.  Empirical Performance of Alternative Option Pricing Models , 1997 .

[9]  Bin Chen,et al.  Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression , 2012 .

[10]  J. MacKinnon,et al.  Econometric Theory and Methods , 2003 .

[11]  Yongmiao Hong,et al.  Generalized Spectral Tests for Conditional Mean Models in Time Series with Conditional Heteroscedasticity of Unknown Form , 2005 .

[12]  Yongmiao Hong,et al.  AN IMPROVED GENERALIZED SPECTRAL TEST FOR CONDITIONAL MEAN MODELS IN TIME SERIES WITH CONDITIONAL HETEROSKEDASTICITY OF UNKNOWN FORM , 2006, Econometric Theory.

[13]  Michael McAleer,et al.  The significance of testing empirical non-nested models , 1995 .

[14]  L. Hansen Large Sample Properties of Generalized Method of Moments Estimators , 1982 .

[15]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[16]  A. I. McLeod,et al.  DIAGNOSTIC CHECKING ARMA TIME SERIES MODELS USING SQUARED‐RESIDUAL AUTOCORRELATIONS , 1983 .

[17]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[18]  D. Rivers,et al.  Model Selection Tests for Nonlinear Dynamic Models , 2002 .

[19]  S. Heston A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[20]  Percy A. Pierre Infinitely divisible distributions, conditions for independence, and central limit theorems , 1971 .

[21]  R. C. Merton,et al.  The impact on option pricing of specification error in the underlying stock price returns , 2011 .

[22]  Torben G. Andersen,et al.  Parametric Inference and Dynamic State Recovery from Option Panels , 2012 .

[23]  R. Cont,et al.  Non-parametric calibration of jump–diffusion option pricing models , 2004 .

[24]  Robert A. Jarrow Risk Management Models: Construction, Testing, Usage , 2011, The Journal of Derivatives.

[25]  Q. Vuong Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses , 1989 .

[26]  Yongmiao Hong,et al.  Hypothesis Testing in Time Series via the Empirical Characteristic Function: A Generalized Spectral Density Approach , 1999 .

[27]  David S. Bates Post-'87 crash fears in the S&P 500 futures option market , 2000 .

[28]  Christian Gourieroux,et al.  Efficient Derivative Pricing by the Extended Method of Moments , 2009 .