From BASEL III to BASEL IV and beyond: Expected shortfall and expectile risk measures |
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| Institution: | 1. Finance, Accounting, and Control, Indian Institute of Management Amritsar, Punjab 143105, India;2. Finance and Accounting, Indian Institute of Management Lucknow, Prabandh Nagar, IIM Road, Lucknow, Uttar Pradesh 226013, India;1. School of Economics and Management, Southwest Jiaotong University, Chengdu, China;2. Service Science and Innovation Key Laboratory of Sichuan Province, China;3. School of Business, Lebanese American University, Lebanon;1. Department of Business Administration, One Academic College, Zahal 104 Street, Kiryat Ono 55000, Israel;2. Plaster School of Business, Missouri Southern State University, Joplin, MO, United States;3. Department of Economics, Texas Tech University, Lubbock, TX, United States |
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| Abstract: | The article contributes to the ongoing search for a market risk measure that is both coherent and elicitable. We compare two traditional measures, namely Value-at-Risk and the expected shortfall, with another relatively novel one established on the expectile probability term. Our research is based on five models: Black–Scholes, exponential tempered stable, Heston, Bates and another stochastic volatility model with a tempered stable jump correction. We apply the general Fourier inversion formula to derive closed form formulas for calculating not only the expectile based risk measure but also the Value-at-Risk and the expected shortfall. These models are calibrated by combining nonlinear programming with simulated annealing at a moving window. Additionally, we compare the generated values of the risk measures with the real ones. Last but not least, we modify the expectile based risk measure as well as the expected shortfall by introducing correction coefficients. |
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| Keywords: | Basel Committee on Banking Supervision Value-at-Risk Expected shortfall Expectile based risk measure Correction coefficients |
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