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Asymptotically distribution-free tests for the volatility function of a diffusion

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  • Chen, Qiang
  • Zheng, Xu
  • Pan, Zhiyuan

Abstract

This paper develops two tests for parametric volatility function of a diffusion model based on Khmaladze (1981)’s martingale transformation. The tests impose no restrictions on the functional form of the drift function and are shown to be asymptotically distribution-free. The tests are consistent against a large class of fixed alternatives and have nontrivial power against a class of root-n local alternatives. The paper also extends the tests of volatility to testing for joint specifications of drift and volatility. Monte Carlo simulations show that the tests perform well in finite samples. The proposed tests are then applied to testing models of short-term interest, using data of Treasury bill rate and Eurodollar deposit rate. The empirical results show that the commonly used CKLS volatility function of Chan et al. (1992) fits volatility function poorly and none of the parametric interest rate models considered in the paper fit data well.

Suggested Citation

  • Chen, Qiang & Zheng, Xu & Pan, Zhiyuan, 2015. "Asymptotically distribution-free tests for the volatility function of a diffusion," Journal of Econometrics, Elsevier, vol. 184(1), pages 124-144.
    • Handle: RePEc:eee:econom:v:184:y:2015:i:1:p:124-144
    DOI: 10.1016/j.jeconom.2014.06.020
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    More about this item

    Keywords

    Distribution-free tests; Volatility function; Diffusion model; Martingale transformation; Monte Carlo simulations; Interest rate volatility;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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