基于幂风险谱和蒙特卡洛模拟的贷款优化配置模型
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摘要
极端风险对于银行资产配置至关重要,尤其是次贷危机之后尾部风险以惨重的代价引起了金融机构的重视,传统条件风险价值CVaR、风险价值VaR不能有效度量尾部极端风险,因此本文基于幂风险谱和蒙特卡洛模拟构建了贷款组合优化配置模型,同时控制尾部极端风险和信用风险。本文一是通过损失-X_i越大、其风险权重φ_i也就越大的思路,构建幂风险谱PSR(Power Spectral Risk)最小的目标函数对极端风险进行控制,即弥补了CVaR同等看待尾部风险、忽略风险较大的损失应予以更大权重的不足,也同时弥补了VaR仅提供某一置信水平下资产损失的最大值、无法反映一旦超过这一数值的可能损失的弊端。二是通过蒙特卡洛模拟信用等级迁移引起贷款收益的变化情景,并以信用等级迁移后贷款组合损失越大、则风险厌恶权重越大的思路构建幂风险谱PSR最小为目标函数,以贷款组合的收益大于目标收益为约束,构建贷款优化配置模型,改变了现有研究贷款配置时没有同时控制信用风险和尾部风险的不足。对比分析结果表明:本文模型能够实现更高的收益风险比,即在单位幂风险谱PSR下能够实现较高的收益。
Extreme risk is very important for bank asset allocation.Especially after the subprime mortgage crisis,the tail risk has drawn great attention from financial institutions.The traditional Conditional Value at Risk(CVaR)and Value at Risk(VaR)cann't measure the tail extreme risk effectively.Therefore,Power Spectral Risk Measure and Monte Carlo simulation are combined to build a portfolio selection model,while controlling tail extreme risk and credit risk.First,through the idea that loss X_i is larger while the risk weight φ_i is larger,the extreme risk is controlled by minimizing the Power Spectral Risk of loan portfolio.This method makes up the shortcoming of CVaR that ignoring the risky losses should be greater weight deficiencies and the shortcoming of VaR that only provides a maximum confidence level of asset loss without reflecting the potential loss more than the confidence level.Second,Monte Carlo simulation is implemented for estimating portfolio credit risk which caused by the credit rating migration.Then,through the idea that the greater the loss of loan portfolio after the credit rating migration,the greater the risk aversion weight is,establish the objective by minimizing the PSR of loan portfolio.The portfolio selection model is constructed by combining the objective of PSR and the constraints that the return of portfolio is greater than the target revenue.The proposed model makes up for the lack of control of credit risk and tail risk in the existing researches.The empirical evidence is based on the historical data of 12 loans.The empirical results show that the proposed model can achieve higher yield risk ratio than CVaR and VaR model,that is,the proposed model can achieve higher profit under the unit power spectral risk.This paper expands the idea of combining loan extreme risk and credit risk for loan allocation
Extreme risk is very important for bank asset allocation.Especially after the subprime mortgage crisis,the tail risk has drawn great attention from financial institutions.The traditional Conditional Value at Risk(CVaR)and Value at Risk(VaR)cann't measure the tail extreme risk effectively.Therefore,Power Spectral Risk Measure and Monte Carlo simulation are combined to build a portfolio selection model,while controlling tail extreme risk and credit risk.First,through the idea that loss X_i is larger while the risk weight φ_i is larger,the extreme risk is controlled by minimizing the Power Spectral Risk of loan portfolio.This method makes up the shortcoming of CVaR that ignoring the risky losses should be greater weight deficiencies and the shortcoming of VaR that only provides a maximum confidence level of asset loss without reflecting the potential loss more than the confidence level.Second,Monte Carlo simulation is implemented for estimating portfolio credit risk which caused by the credit rating migration.Then,through the idea that the greater the loss of loan portfolio after the credit rating migration,the greater the risk aversion weight is,establish the objective by minimizing the PSR of loan portfolio.The portfolio selection model is constructed by combining the objective of PSR and the constraints that the return of portfolio is greater than the target revenue.The proposed model makes up for the lack of control of credit risk and tail risk in the existing researches.The empirical evidence is based on the historical data of 12 loans.The empirical results show that the proposed model can achieve higher yield risk ratio than CVaR and VaR model,that is,the proposed model can achieve higher profit under the unit power spectral risk.This paper expands the idea of combining loan extreme risk and credit risk for loan allocation
引文
[1]刘艳萍，曲蕾蕾．基于下偏度最小化贷款组合优化模型[J]．中国管理科学，2014,22(2):32-39．
[2]Artzner P,Delbaen F,Eber J M,et al.Thinking coherently:Generalised scenarios rather than var should be used when calculating regulatory capital[J].Risk London Risk Magazine Limited,1997,10(11):68-71．
[3]刘艳萍，王婷婷，迟国泰．基于风险价值约束的贷款组合效用最大化优化模型[J]．系统管理学报，2009,18(2):121-129．
[4]匡海波，张一凡，张连如．低碳港口物流质押贷款组合优化决策模型[J]．系统工程理论与实践，2014,34(6):1468-1479．
[5]Lwin K T,Qu R,MacCarthy B L.Mean-VaR portfolio optimization:A nonparametric approach[J].European Journal of Operational Research,2017,260(2):751-766．
[6]Rockafellar R T,Uryasev S.Optimization of conditional value-at-risk[J].Journal of risk,2000,2:21-42．
[7]Andersson F,Mausser H,Rosen D,et al.Credit risk optimization with conditional value-at-risk criterion[J].Mathematical Programming,2001,89(2):273-291．
[8]Alexander S,Coleman T F,Li Y.Minimizing CVaRand VaR for a portfolio of derivatives[J].Journal of Banking&Finance,2006,30(2):583-605．
[9]Najafi A A,Mushakhian S.Multi-stage stochastic mean-semivariance-CVaR portfolio optimization under transaction costs[J].Applied Mathematics and Computation,2015,256(7):445-458．
[10]Gao Jianjun,Zhou Ke,Li Duan,et al.Dynamic mean-LPM and mean-CVaR portfolio optimization in continuous-time[J].SIAM Journal on Control and Optimization,2017,55(3):1377-1397．
[11]Acerbi C.Spectral measures of risk:A coherent representation of subjective risk aversion[J].Journal of Banking&Finance,2002,26(7):1505-1518．
[12]Acerbi C,Prospero S.Portfolio optimization with spectral measures of risk[J].Quantitative Finance,2002,79(7):1-28．
[13]Cotter J,Dowd K.Exponential spectral risk measures[J].Mpra Paper,2007,4:57-66．
[14]Adam A,Houkari M,Laurent J P.Spectral risk measures and portfolio selection[J].Journal of Banking&Finance,2008,32(9):1870-1882．
[15]Lim A E B.Conditional value-at-risk in portfolio optimization:Coherent but fragile[J].Operations Research Letters,2011,39(3):163-171．
[16]韩萱，杨永愉．混合型风险谱函数的谱风险度量[J]．北京化工大学学报（自然科学版），2013,40(5):110-116．
[17]Abad C,Iyengar G.Portfolio selection with multiple spectral risk constraints[J].SIAM Journal on Financial Mathematics,2015,6(1):467-486．
[18]刁训娣，童斌，吴冲锋．基于EVT的谱风险测度及其在风险管理中的应用[J]．系统工程学报，2015,30(3):354-369+405．
[19]马志卫，刘应宗．基于蒙特卡洛模拟的贷款组合优化决策方法[J]．管理科学，2006,19(3):66-70．
[20]司继文，张明佳，龚朴．基于Monte Carlo模拟和混合整数规划的CVaR(VaR）投资组合优化[J]．武汉理工大学学报（交通科学与工程版），2005,3(29):411-414．
[21]Balbás A,Garrido J,Mayoral S.Properties of distortion risk measures[J].Methodology and Computing in Applied Probability,2009,11(3):385．
[22]王秀国，邱菀华．基于CVaR和Monte Carlo仿真的贷款组合决策模型[J]．计算机工程与应用，2007,43(4):26-29．
[23]Morgan J P.CreditMetrics-technical document[R].Working Paper,Jp Morgan,1997.
[2]Artzner P,Delbaen F,Eber J M,et al.Thinking coherently:Generalised scenarios rather than var should be used when calculating regulatory capital[J].Risk London Risk Magazine Limited,1997,10(11):68-71．
[3]刘艳萍，王婷婷，迟国泰．基于风险价值约束的贷款组合效用最大化优化模型[J]．系统管理学报，2009,18(2):121-129．
[4]匡海波，张一凡，张连如．低碳港口物流质押贷款组合优化决策模型[J]．系统工程理论与实践，2014,34(6):1468-1479．
[5]Lwin K T,Qu R,MacCarthy B L.Mean-VaR portfolio optimization:A nonparametric approach[J].European Journal of Operational Research,2017,260(2):751-766．
[6]Rockafellar R T,Uryasev S.Optimization of conditional value-at-risk[J].Journal of risk,2000,2:21-42．
[7]Andersson F,Mausser H,Rosen D,et al.Credit risk optimization with conditional value-at-risk criterion[J].Mathematical Programming,2001,89(2):273-291．
[8]Alexander S,Coleman T F,Li Y.Minimizing CVaRand VaR for a portfolio of derivatives[J].Journal of Banking&Finance,2006,30(2):583-605．
[9]Najafi A A,Mushakhian S.Multi-stage stochastic mean-semivariance-CVaR portfolio optimization under transaction costs[J].Applied Mathematics and Computation,2015,256(7):445-458．
[10]Gao Jianjun,Zhou Ke,Li Duan,et al.Dynamic mean-LPM and mean-CVaR portfolio optimization in continuous-time[J].SIAM Journal on Control and Optimization,2017,55(3):1377-1397．
[11]Acerbi C.Spectral measures of risk:A coherent representation of subjective risk aversion[J].Journal of Banking&Finance,2002,26(7):1505-1518．
[12]Acerbi C,Prospero S.Portfolio optimization with spectral measures of risk[J].Quantitative Finance,2002,79(7):1-28．
[13]Cotter J,Dowd K.Exponential spectral risk measures[J].Mpra Paper,2007,4:57-66．
[14]Adam A,Houkari M,Laurent J P.Spectral risk measures and portfolio selection[J].Journal of Banking&Finance,2008,32(9):1870-1882．
[15]Lim A E B.Conditional value-at-risk in portfolio optimization:Coherent but fragile[J].Operations Research Letters,2011,39(3):163-171．
[16]韩萱，杨永愉．混合型风险谱函数的谱风险度量[J]．北京化工大学学报（自然科学版），2013,40(5):110-116．
[17]Abad C,Iyengar G.Portfolio selection with multiple spectral risk constraints[J].SIAM Journal on Financial Mathematics,2015,6(1):467-486．
[18]刁训娣，童斌，吴冲锋．基于EVT的谱风险测度及其在风险管理中的应用[J]．系统工程学报，2015,30(3):354-369+405．
[19]马志卫，刘应宗．基于蒙特卡洛模拟的贷款组合优化决策方法[J]．管理科学，2006,19(3):66-70．
[20]司继文，张明佳，龚朴．基于Monte Carlo模拟和混合整数规划的CVaR(VaR）投资组合优化[J]．武汉理工大学学报（交通科学与工程版），2005,3(29):411-414．
[21]Balbás A,Garrido J,Mayoral S.Properties of distortion risk measures[J].Methodology and Computing in Applied Probability,2009,11(3):385．
[22]王秀国，邱菀华．基于CVaR和Monte Carlo仿真的贷款组合决策模型[J]．计算机工程与应用，2007,43(4):26-29．
[23]Morgan J P.CreditMetrics-technical document[R].Working Paper,Jp Morgan,1997.
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