最小化CVaR对冲问题的随机分形搜索算法求解
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摘要
在考虑交易费用情形下和在给定初始成本约束条件下,针对期权对冲问题,采用条件风险价值来刻画损失风险,基于跳-扩散模型建立动态随机优化模型,并探寻用随机分形搜索算法来求解该非线性优化问题,获得最优对冲策略。数值模拟算例和实证研究的结果表明随机分形搜索算法求解最小化CVaR对冲问题是可行和有效的。
In this paper,based on the jump diffusion model,we consider the problem of hedging conditional value at risk of contingent claims on a stock under transaction costs and given initial cost.A dynamic stochastic optimization model is established,and Stochastic Fractal Search is used to solve the nonlinear optimization problem to obtain the optimal hedging strategy.The results of numerical simulation and empirical research show that Stochastic Fractal Search is feasible and effective for solving the hedging problem by minimum CVaR.
In this paper,based on the jump diffusion model,we consider the problem of hedging conditional value at risk of contingent claims on a stock under transaction costs and given initial cost.A dynamic stochastic optimization model is established,and Stochastic Fractal Search is used to solve the nonlinear optimization problem to obtain the optimal hedging strategy.The results of numerical simulation and empirical research show that Stochastic Fractal Search is feasible and effective for solving the hedging problem by minimum CVaR.
引文
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[2]Schweizer M.A Guided Tour Through Quadratic Hedging Approaches[C]//Jouini E et al.Option Pricing Interest Rates and Risk Management.Cambridge:Cambridge University Press,2010:538-574.
[3]F9llmer H,Leukert P.Quantilehedging[J].Finance and Stochastics,1999,3(3):251-273.
[4]F9llmer H,Leukert P.Efficient Hedging:Cost Versus Shortfall Risk[J].Finance and Stochastics,2000,4(2):117-146.
[5]黄金波,郑军,丁杰,等.VaR测度下的风险对冲策略研究[J].运筹与管理,2017,26(3):138-147.
[6]Morgan J P.RiskMetrics Technical Document[M].4thed.New York:Morgan Guaranty Trust Company,1996.
[7]Rockafellar R T,Uryasev S.Optimization of Conditional Value-At-Risk[J].Journal of Risk,1999,29(1):1071–1074.
[8]Topaloglou N,Vladimirou H,Zenios S A.CVaR Models with Selective Hedging for International Asset Allocation[J].Journal of Banking&Finance,2002,26(7):1535-1561.
[9]Li J,Xu M.Risk Minimizing Portfolio Optimization and Hedging with Conditional Value-at-risk[J].Review of Futures Markets 2008(16):471-506.
[10]迟国泰,赵光军,杨中原.基于CVaR的期货最优套期保值比率模型及应用[J].系统管理学报,2009,18(1):27-33.
[11]费广平,孙燕红.最小CVaR股指期货套期保值比率的实证研究[J].统计与决策,2013(8):156-159.
[12]黄金波,李仲飞.分布不确定下的风险对冲策略及其效用[J].中国管理科学,2017,25(1):1-10.
[13]Tarnopolskaya T,Zhu Z.CVaR-minimising Hedging by a Smoothing Method[J].Anziam Journal,2010,52(C):237-256.
[14]张清叶,高岩.基于CVaR投资组合优化问题的非光滑优化方法[J].中国管理科学,2017(10):11-19.
[15]Salimi H.Stochastic Fractal Search:A Powerful Metaheuristic Algorithm[J].Knowledge-Based Systems,2015(75):1-18.
[2]Schweizer M.A Guided Tour Through Quadratic Hedging Approaches[C]//Jouini E et al.Option Pricing Interest Rates and Risk Management.Cambridge:Cambridge University Press,2010:538-574.
[3]F9llmer H,Leukert P.Quantilehedging[J].Finance and Stochastics,1999,3(3):251-273.
[4]F9llmer H,Leukert P.Efficient Hedging:Cost Versus Shortfall Risk[J].Finance and Stochastics,2000,4(2):117-146.
[5]黄金波,郑军,丁杰,等.VaR测度下的风险对冲策略研究[J].运筹与管理,2017,26(3):138-147.
[6]Morgan J P.RiskMetrics Technical Document[M].4thed.New York:Morgan Guaranty Trust Company,1996.
[7]Rockafellar R T,Uryasev S.Optimization of Conditional Value-At-Risk[J].Journal of Risk,1999,29(1):1071–1074.
[8]Topaloglou N,Vladimirou H,Zenios S A.CVaR Models with Selective Hedging for International Asset Allocation[J].Journal of Banking&Finance,2002,26(7):1535-1561.
[9]Li J,Xu M.Risk Minimizing Portfolio Optimization and Hedging with Conditional Value-at-risk[J].Review of Futures Markets 2008(16):471-506.
[10]迟国泰,赵光军,杨中原.基于CVaR的期货最优套期保值比率模型及应用[J].系统管理学报,2009,18(1):27-33.
[11]费广平,孙燕红.最小CVaR股指期货套期保值比率的实证研究[J].统计与决策,2013(8):156-159.
[12]黄金波,李仲飞.分布不确定下的风险对冲策略及其效用[J].中国管理科学,2017,25(1):1-10.
[13]Tarnopolskaya T,Zhu Z.CVaR-minimising Hedging by a Smoothing Method[J].Anziam Journal,2010,52(C):237-256.
[14]张清叶,高岩.基于CVaR投资组合优化问题的非光滑优化方法[J].中国管理科学,2017(10):11-19.
[15]Salimi H.Stochastic Fractal Search:A Powerful Metaheuristic Algorithm[J].Knowledge-Based Systems,2015(75):1-18.