A0972
Title: Analysis of value-at-risk and expected shortfall under a jump-diffusion model with left-skewed jump sizes
Authors: Xenos Chang-Shuo Lin - Aletheia University (Taiwan)
Having Yi-Ju Chien - University of Texas at Arlington (United States)
Wei-Chung Miao - National Taiwan University of Science and Technology (Taiwan) [presenting]
Abstract: A jump-diffusion model is proposed which incorporates the left skewedjump size distribution and discuss the effects of the left skewness in jump sizes on the two major risk measures: Value-at-Risk (VaR) and Expected Shortfall (ES). The jump size distribution is described by a shifted gamma (SG) distribution and our proposed jump-diffusion model (termed SGJD model) can be seen as an extended version of the classical jump-diffusion model. We provide mathematical analysis of the proposed model and derive analytical formulas for the two risk measures under our model. Since a new parameter is introduced to capture jump size skewness and Merton's classical model is actually a limiting case with skewness parameter approaching 0, our numerical analysis examines how the return distributions and VaR/ES vary as the skewness parameter deviates from 0. Our results show that the skewness parameter plays a significant role in VaR and ES, particularly when the time interval is small and confidence level is high. These observations justify the incorporation of the left skewed jump size and provide supports for the proposed SGJD model when the far left end of the return distribution is concerned.
