Sensitivity analysis of VaR and Expected Shortfall for portfolios under netting agreements |
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| Institution: | 1. CDC Ixis Capital Markets, 47 quai d’Austerlitz, 75648 Paris Cedex 13, France;2. CREST, 15 bd Gabriel Péri, 92245 Malakoff Cedex, France;3. HEC Genève and FAME, UNIMAIL, Faculté des SES, Université de Genève, 102 Boulevard Carl Vogt, Genève 4CH-1211, Switzerland;1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China;2. School of Mathematics, University of Manchester, Manchester, United Kingdom;3. Institute of Mathematics, School of Mathematics Sciences, Nanjing Normal University, Nanjing, 210097, China;1. Department of Economics and Finance, City University of Hong Kong, Kowloon, Hong Kong;2. Robert H. Smith School of Business and Institute for Systems Research, University of Maryland, College Park, MD, 20742, USA;3. Department of Mathematics, Tongji University, Shanghai, 200092, China;1. Department of Statistics and Finance, University of Science and Technology of China, Hefei, Anhui 230026, China;2. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L3G1, Canada |
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| Abstract: | In this paper, we characterize explicitly the first derivative of the Value at Risk and the Expected Shortfall with respect to portfolio allocations when netting between positions exists. As a particular case, we examine a simple Gaussian example in order to illustrate the impact of netting agreements in credit risk management. Collateral issues are also dealt with. For practical purposes we further provide nonparametric estimators for sensitivities and derive their asymptotic distributions. An empirical application on a typical banking portfolio is finally provided. |
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