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Testing the diffusion coefficient

Author

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  • Kleinow, Torsten

Abstract

In mathematical finance diffusion models are widely used and a variety of different parametric models for the drift and diffusion coefficient coexist in the literature. Since derivative prices depend on the particular parametric model of the diffusion coefficient function of the underlying, a misspecification of this function leads to misspecified option prices. We develop two tests about a parametric form of the diffusion coefficient. The finite sample properties of the tests are investigated in a simulation study and the tests are applied to the 7 -day Eurodollar rate, the German stock market index DAX and five German stocks. For all observed processes, we find in the empirical analysis that our tests reject all tested parametric models. We conclude that affine diffusion processes might not be appropriate to model the evolution of financial time series and that a successful model for a financial market should incorporate the history of the observed processes of additional sources of randomness like stochastic volatility models.

Suggested Citation

  • Kleinow, Torsten, 2002. "Testing the diffusion coefficient," SFB 373 Discussion Papers 2002,38, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200238
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    Citations

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    Cited by:

    1. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
    2. Holger Dette & Mark Podolskij & Mathias Vetter, 2006. "Estimation of Integrated Volatility in Continuous‐Time Financial Models with Applications to Goodness‐of‐Fit Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 259-278, June.
    3. Papanicolaou, Alex & Giesecke, Kay, 2016. "Variation-based tests for volatility misspecification," Journal of Econometrics, Elsevier, vol. 191(1), pages 217-230.

    More about this item

    Keywords

    Diffusion; Continuous-time financial models; Nonparametric methods; Kernel smoothing; Goodness of fit test; spot rate models; interest rate; stock market index; Empirical Likelihood;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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