Comparing the Frechet Distribution and the Generalized Pareto Distribution in Estimating Value at Risk and Conditional Value at Risk in Tehran Stock Exchange

Selecting the most accurate method of risk measurement is the main challenge in risk estimation. This study aims to measure value at risk (VaR) and conditional value at risk (CoVar) in Tehran Stock Exchange (TSE) using the Frechet distribution (FD) and the generalized Pareto distribution (GPD). It used the data from 21 and 63-day time series of TEPIX, free-float, and the indices of the top 50 TSE companies between 2012-3-20 and 2020-3-19. It used COPIC post-test and Christoffersen’s conditional coverage test for models statistical confirmation. It applied Lopez and Blanco-Ihle’s second loss functions for model comparison. The CoVaR models were ranked by two loss functions, including Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). Results indicated according to the statistics measured in Lopez’s second loss function, GPD performed better than FD in measuring VaR of TEPIX and the return index of the selected 50 companies, however, FD performed better for the free-float index. Blanco-Ihle’s loss function results contradicted the ones derived from Lopez’s second loss function. MAE and RMSE results indicated FD is better in estimating CoVaR.