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In this paper, an approximate version of the Barndorff-Nielsen and Shephardmodel, driven by a Brownian motion and a L\'evy subordinator, is formulated.The first-exit time of the log-return process for this model is analyzed. It isshown that with certain probability, the first-exit time process of thelog-return is decomposable into the sum of the first exit time of the Brownianmotion with drift, and the first exit time of a L\'evy subordinator with drift.Subsequently, the probability density functions of the first exit time of somespecific L\'evy subordinators, connected to stationary, self-decomposablevariance processes, are studied. Analytical expressions of the probabilitydensity function of the first-exit time of three such L\'evy subordinators areobtained in terms of various special functions. The results are implemented toempirical S&P 500 dataset.

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