Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models

Abstract

This paper attempted to calculate the market risk in the Tehran Stock Exchange by estimating the Conditional Value at Risk. Since the Conditional Value at Risk is a tail-related measure, Extreme Value Theory has been utilized to estimate the risk more accurately. Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models were used to model the volatility-clustering feature, and to estimate the parameters of the model, the Maximum Likelihood method was applied. The results of the study showed that in the estimation of model parameters, assuming T-student distribution function gave better results than the Normal distribution function. The Monte Carlo simulation method was used for backtesting the Conditional Value at Risk model, and in the end, the performance of different models, in the estimation of this measure, was compared.

Keywords

• conditional value at risk
• extreme value theory
• GARCH models
• backtesting models
• maximum likelihood method