Model Calibration by Matching to the Empirical Distribution

• Activity Number: 270
• Type: Invited
• Date/Time: Tuesday, August 5, 2003 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): A. Ronald Gallant*+
• Companies: Duke University
• Keywords: asset pricing ; calibration ; EDF ; MCMC

Abstract

We consider Markovian economic models of financial markets. Being Markovian, all sample information is contained in the empirical distribution of contemporaneous and lagged values of the data. These models are solved numerically via simulation methods. Since model solution produces a simulation, it is natural to calibrate the model by comparing the empirical distribution of a simulation to the empirical distribution of the sample by means of a Cramer-von Mises statistic. The model is calibrated by adjusting its parameters to minimize the statistic. This is a nonsmooth optimization problem that is solved by MCMC methods. An interesting and novel aspect of this approach is that the stationary distribution of the MCMC simulation is the same as the frequentist's sampling distribution of parameter estimates. Thus frequentist confidence intervals on features of the model are readily obtained without the necessity of bootstrapping or similar computationally intensive strategies. The methodology is also well-suited to imposing moment restrictions such as a zero-real-risk-free rate or prespecified risk premia on the economic model.