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arXiv · 2006.07167

First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process

Shantanu Awasthi·Indranil SenGupta
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Abstract

In this paper, an approximate version of the Barndorff-Nielsen and Shephard model, driven by a Brownian motion and a Lévy subordinator, is formulated. The first-exit time of the log-return process for this model is analyzed. It is shown that with certain probability, the first-exit time process of the log-return is decomposable into the sum of the first exit time of the Brownian motion with drift, and the first exit time of a Lévy subordinator with drift. Subsequently, the probability density functions of the first exit time of some specific Lévy subordinators, connected to stationary, self-decomposable variance processes, are studied. Analytical expressions of the probability density function of the first-exit time of three such Lévy subordinators are obtained in terms of various special functions. The results are implemented to empirical S&P 500 dataset.

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Shantanu Awasthi, Indranil SenGupta. 2021-01-07. First exit-time analysis for an approximate Barndorff-Nielsen and Shephard model with stationary self-decomposable variance process. https://doi.org/10.31390/josa.2.1.05

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