Path Risk Measure PMVaR:Properties And Empirical Research

One of the key roles of risk management is to measure the market loss(risk)based on market information.Based on the measured risks,financial institutions can prepare sufficient capital reserves to save potential losses,so that normal financial activities can be maintained when the market is going down in the near future.At a given time interval,the traditional risk measure VaR is the minimum value of financial assets returns,which mainly has the following deficiencies:Based on the quantile of the return sequence,VaR ignores the tail risk;VaR does not have subadditivity;Considering the time interval n,the calculation of VaR is based on the revaluated asset price of n working days,which cannot reflect the minimum return(the maximum risk)generated by the change of asset price in each time segment.Basel III proposed to increase the capital adequacy ratio by about 23%.The definition of the path is introduced in this paper because VaR cannot mea-sure the maximum risk in the risk assessment for the time interval n.Based on path,we define the path risk measure VaR for the traditional VaR of time interval n.Con-sidering the minimum revenue that may occur during the interval,the path risk mea-sure PMVaR is proposed.From theoretical and Monte Carlo simulations aspects,this paper proves that PMVaR is larger than VaR,which has translation invariance,monotonicity,and is subadditive for multivariate normal distributions and multivariate regular variations.From the view of Monte Carlo simulation and actual data,it proves that the relative increasement ratio of PMVaR pairs VaR is about 20%,which satis-fies the capital adequacy ratio requirements of Basel III.Finally,the backtesting results of PMVaR of the S&P500 index daily returns data show that the financial data can be fitted by AR(1)-GARCH(1,1)model with innovations Student t distribution well,and PMVaR can measure the risk of a minimum return of time interval n better.