Application of conditional value at risk for credit risk optimization
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Mar 22, 2017
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Abstract
The article is dedicated to the optimization of credit risk through the application of Conditional Value at Risk (CVaR). CVaR is a risk measure, the expected loss exceeding Value-at-Risk and is also known as Mean Excess, Mean Shortfall, or Tail VaR. The link between credit risk and the current financial crisis accentuates the importance of measuring and predicting extreme credit risk. Conditional Value at Risk has become an increasingly popular method for measurement and optimization of extreme market risk. The use of model can regulate all positions in a portfolio of financial instruments in order to minimize CVaR subject to trading and return constraints at the same time. The credit risk distribution is created by Monte Carlo simulations and the optimization problem is solved effectively by linear programming. We apply these CVaR techniques to the optimization of credit risk on portfolio of selected bonds.
Keywords: value at risk; conditional value at risk; credit risk; portfolio
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References
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Andersson, F., Uryasev, S., Mausser, H. & Rosen, D. (2000). Credit risk optimization with conditional value-at risk criterion. Mathematical Programming, 89 (2), 273-291.
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Grublova, E. (2010). Attitudes to risk and ability to take risky decisions. Ekonomicko-manazerske spektrum, 4 (2), 58-63.
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Kollar, B. & Bartosova, V. (2014). Comparison of credit risk measures as an alternative to VaR. 2nd International Conference on Social Sciences Research (SSR 2014), Advances in Social and Behavioral Sciences, 5, 167 – 171.
Kollar, B., Valaskova, K. & Kramarova, K. (2015). Possibility of using credit grades model as an alternative to traditional structural models, 3rd International Conference on Economics and Social Science (ICESS 2015), Advances in Education Research, 86, 53 – 58.
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Rockafellar, R. T. & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, 26 (7), 1443-1471
Uryasev, S. (2000). Conditional value-at-risk: Optimization algorithms and applications. Financial Engineering News (14 February): 1–5.
Valaskova, K., Gavlakova, P. & Dengov, V. (2014). Assessing credit risk by Moody's KMV Model, 2nd International Conference on Economics and Social Science (ICESS), Advances in Education Research 61, 40-44.
Wilson, T. (1997). Portfolio credit risk I, Risk, 10 (9), 111-117.
Wilson, T. (1997). Portfolio credit risk II, Risk, 10 (10), 56-61.
Yamai, Y. & Yoshiba, T. (2002). Comparative analysis of expected shortfall and value-at-risk: Their estimation error, decomposition and optimization. Monetary and Economic Studies, 20 (1). 57–86.
Andersson, F., Uryasev, S., Mausser, H. & Rosen, D. (2000). Credit risk optimization with conditional value-at risk criterion. Mathematical Programming, 89 (2), 273-291.
Buc, D. & Kliestik, T. (2013). Aspects of statistics in terms of financial modelling and risk. 7th International Days of Statistics and Economics, Prague, Czech Republic, 215-224.
Dengov, V. V. & Gregova, E. (2010). Economic decision-making under uncertainty and risk. Methodology and criteria for decision-making. Ekonomicko-manazerske spektrum, 4 (2), 28-45.
Frajtova-Michalikova, K., Kliestik, T. & Musa, H. (2015). Comparison of nonparametric methods for estimating the level of risk in finance. Procedia Economics and finance, 24, 228 – 236.
Gavlakova, P. & Kliestik, T. (2014). Credit risk models and valuation, 4th International Conference on Applied Social Science (ICASS), Advances in Education Research 51, 139-143.
Grublova, E. (2010). Attitudes to risk and ability to take risky decisions. Ekonomicko-manazerske spektrum, 4 (2), 58-63.
Kliestik, T., Musa, H. & Frajtova-Michalikova, K. (2015). Parametric methods for estimating the level of risk in finance. Procedia Economics and finance, 24, 322 – 330.
Kollar, B. & Bartosova, V. (2014). Comparison of credit risk measures as an alternative to VaR. 2nd International Conference on Social Sciences Research (SSR 2014), Advances in Social and Behavioral Sciences, 5, 167 – 171.
Kollar, B., Valaskova, K. & Kramarova, K. (2015). Possibility of using credit grades model as an alternative to traditional structural models, 3rd International Conference on Economics and Social Science (ICESS 2015), Advances in Education Research, 86, 53 – 58.
Kral, P. & Kliestik, T. (2015). Estimation of the level of risk based on the selected theoretical probability distributions, 10th International Scientific Conference Financial management of Firms and Financial Institutions, Ostrava, Czech Republic, 603-610.
Larsen, N., Mausser, H. & Uryasev, S. (2000). Algorithms for optimization of value-at-risk. Financial Engineering, e-Commerce and Supply Chain. Kluwer Academic Publishers, Dordrecht, Netherlands, 129–157.
Rockafellar, R. T. & Uryasev, S. (2002). Conditional value-at-risk for general loss distributions. Journal of Banking and Finance, 26 (7), 1443-1471
Uryasev, S. (2000). Conditional value-at-risk: Optimization algorithms and applications. Financial Engineering News (14 February): 1–5.
Valaskova, K., Gavlakova, P. & Dengov, V. (2014). Assessing credit risk by Moody's KMV Model, 2nd International Conference on Economics and Social Science (ICESS), Advances in Education Research 61, 40-44.
Wilson, T. (1997). Portfolio credit risk I, Risk, 10 (9), 111-117.
Wilson, T. (1997). Portfolio credit risk II, Risk, 10 (10), 56-61.
Yamai, Y. & Yoshiba, T. (2002). Comparative analysis of expected shortfall and value-at-risk: Their estimation error, decomposition and optimization. Monetary and Economic Studies, 20 (1). 57–86.