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Distributional properties of continuous time processes: from CIR to bates

Author

Listed:
  • Ostap Okhrin

    (Chair of Statistics and Econometrics esp. Transportation, Technische Universität Dresden)

  • Michael Rockinger

    (University of Lausanne)

  • Manuel Schmid

    (Chair of Statistics and Econometrics esp. Transportation, Technische Universität Dresden)

Abstract

In this paper, we compute closed-form expressions of moments and comoments for the CIR process which allows us to provide a new construction of the transition probability density based on a moment argument that differs from the historic approach. For Bates’ model with stochastic volatility and jumps, we show that finite difference approximations of higher moments such as the skewness and the kurtosis are unstable and, as a remedy, provide exact analytic formulas for log-returns. Our approach does not assume a constant mean for log-price differentials but correctly incorporates volatility resulting from Ito’s lemma. We also provide R, MATLAB, and Mathematica modules with exact implementations of the theoretical conditional and unconditional moments. These modules should prove useful for empirical research.

Suggested Citation

  • Ostap Okhrin & Michael Rockinger & Manuel Schmid, 2023. "Distributional properties of continuous time processes: from CIR to bates," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 397-419, September.
    • Handle: RePEc:spr:alstar:v:107:y:2023:i:3:d:10.1007_s10182-022-00459-3
    DOI: 10.1007/s10182-022-00459-3
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    References listed on IDEAS

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    More about this item

    Keywords

    Higher moments; Distributional properties; Stochastic volatility; Jump diffusion; CIR process; Square-root process;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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