Distributional properties of continuous time processes: from CIR to bates

Ostap Okhrin (), Michael Rockinger () and Manuel Schmid ()
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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

AStA Advances in Statistical Analysis, 2023, vol. 107, issue 3, No 2, 397-419

Abstract: 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.

Keywords: Higher moments; Distributional properties; Stochastic volatility; Jump diffusion; CIR process; Square-root process (search for similar items in EconPapers)
JEL-codes: C58 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10182-022-00459-3

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