Estimation of Conditional Value at Risk under Stochastic Volatility Levy Processes for Tehran Stock Market

Research has shown that stochastic volatility and jumps play an important role in stock price trends market, and considering these two factors has a significant impact on a better description of assets. Infinite jump Levy processes cover skewness and heavy-tailedness properties but can not present volatility clustering. By time chainging these processes by integrating the Cox-Ingersoll-Ross, it is abtained a stochastic volatility Levy processes model that are applied to determine the conditional value at risk (VaR) in this paper. Applying the fast Fourier transform, a closed form formula of probability density function is derived. Moreover, by applying Hybrid Particle Swarm Optimization algorithm, Grid search method and univariate method algorithm, the parameters are estimated. Based on the introduced model, we estimate the VaR of along total Index of Tehran Stock Exchange in 1388 to 1398 and compare it by historical simulation and Variance-Covariance approaches. The results of Back-test techniques in computing the VaR indicate that the stochastic volatility Levy processes with infinite jumps have better performance than the Variance-Covariance methods.