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.
%0 Journal Article
%1 Okhrin2023continuoustimeprocesses
%A Okhrin, Ostap
%A Rockinger, Michael
%A Schmid, Manuel
%D 2023
%J AStA Advances in Statistical Analysis
%K topic_engineering CIR Distributional Higher Jump Squar Stochastic diffusion moments process properties volatility
%N 3
%P 397-419
%R 10.1007/s10182-022-00459-
%T Distributional properties of continuous time processes: from CIR to bates
%U https://ideas.repec.org/a/spr/alstar/v107y2023i3d10.1007_s10182-022-00459-3.html
%V 107
%X 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.
@article{Okhrin2023continuoustimeprocesses,
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.},
added-at = {2024-11-12T14:23:40.000+0100},
author = {Okhrin, Ostap and Rockinger, Michael and Schmid, Manuel},
biburl = {https://puma.scadsai.uni-leipzig.de/bibtex/2b3a9c065d159cea519f647a7412ad2e4/scadsfct},
doi = {10.1007/s10182-022-00459-},
interhash = {a3750e408af5c91ea2992f8b4f97e29a},
intrahash = {b3a9c065d159cea519f647a7412ad2e4},
journal = {AStA Advances in Statistical Analysis},
keywords = {topic_engineering CIR Distributional Higher Jump Squar Stochastic diffusion moments process properties volatility},
month = {September},
number = 3,
pages = {397-419},
timestamp = {2024-11-22T15:45:28.000+0100},
title = {Distributional properties of continuous time processes: from CIR to bates},
url = {https://ideas.repec.org/a/spr/alstar/v107y2023i3d10.1007_s10182-022-00459-3.html},
volume = 107,
year = 2023
}
