Estimation value at risk (VAR) and conditional value at risk (CoVaR) at Tehran Stock Exchange by approach to using Fréchet distribution (FD)

Risk estimation cannot deliver appropriate reliable predictions by focusing on one or two models and considering the irrelevant factors. This study aims to estimate the value at risk (VAR) and the conditional value at risk (CoVaR) in the Tehran Stock Exchange using Fréchet distribution (FD). In doing so, generalized extreme value (GEV) is used with the help of Friche distribution approach. In this study, the return of 21-day and 63-day data of the time series of the total index, free-float-stock index, and index of 50 active companies of Tehran Stock Exchange during 01/01/2012 to 12/29/1398 have been used. The obtained results through the estimation of three parameters of GEV, including location, scale, and shape, have shown that the parameter of distribution shape within all 21 and 63-day periods of each indicator is positive, and the distribution for indexes studied follows FD as the second type of generalized distribution of GEV. By using the same pattern, the measurement of CoVaR and VaR has presented that it is possible to estimate CoVar and VaR through the use of FD and CoVaR is higher than VaR within the whole range of alpha.