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Specification Analysis of Continuous Time Models in Finance

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  • Gallant, A. Ronald
  • Tauchen, George E.

Abstract

The paper describes the use of the Gallant-Tauchen efficient method of moments (EMM) technique for diagnostic checking of stochastic differential equations (SDEs) estimated from financial market data. The EMM technique is a simulation-based method that uses the score function of an auxiliary model as the criterion to define a generalized method of moments (GMM) objective function. The technique can handle multivariate SDEs where the state vector is not completely observed. The optimized GMM objective function is distributed as chi-square and may be used to test model adequacy. Elements of the score function correspond to specific parameters and large values reflect features of data that a rejected SDE specification does not describe well. The diagnostics are illustrated by estimating a three-factor model to weekly, 1962-1995, term structure data comprised of short (3 month), medium (12 month), and long (10 year) Treasury rates. The Yield-Factor Model is sharply rejected, although an extension that permits the local variance function to be a convex function of the interest rates comes much closer to describing the data.

Suggested Citation

  • Gallant, A. Ronald & Tauchen, George E., 1995. "Specification Analysis of Continuous Time Models in Finance," Working Papers 95-49, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:95-49
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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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