CVaR在金融工具复制上的应用

CVaR Applying on Financial Instrument Replication

RockafellarRT,SUryasev将CVaR应用于金融工具的复制,其结论是CVaR能有效地改善复制的组合.本文在他们研究的基础上,对其方法进行了改进,并将其应用于对中信指数的复制,探讨CVaR的理论意义与实际效果.在对中信指数进行复制的过程中采用了样本区间内模拟和样本区间外模拟,并将两种方法进行了比较.计算结果表明,可以通过一个线性优化问题将CVaR约束考虑到复制的组合中,CVaR的值可以直接由一个线性函数确定,不用先计算VaR的值.而且,当CVaR约束有效时VaR是确定组合的副产品.最重要的发现是,CVaR中损失函数对于控制复制组合的偏离方向有直接作用,RockafellarRT,SUryasev的方法对于样本区间外的模拟是不起作用的;改进的方法对于样本区间外的模拟中CVaR约束是起作用的.

CVaR(Conditional Value-at-Risk) is a new measure of risk based on VaR(Value-at Risk), which has good mathematic properties, can embody characters of risk. Rockafellar R.T., S.Uryasev(2002) applied CVaR on financial instrument replication, and concluded that CVaR can improve portfolio of replication. This paper is,based on their study, mends their method, applies it on replication of Citic Index and discusses the academic significations and practical effects. The replication of Citic Index is conduced in in-sample calculation and out-sample calculation, and compares two methods. The results implies that we can add CVaR restrict into portfolio of replication by a LP problem, can achieve CVaR from a linear function directly without first calculating VaR. Furthermore, when CVaR restrict is effective, VaR can be obtained instead as a byproduct by determining portfolio of replication. The most important discovery is that the loss function of CVaR has effect on controlling deviation of portfolio, the method of Rockafellar R.T., S.Uryasev(2002)is of no effect in out-sample calculation, but the improved method is availability in out-sample calculation.