Modeling the latent Volatilities of the stock exchange index using the copula-stochastic Volatility model

In this study, a hybrid copula-stochastic volatility model based on Monte-Carlo Markov chain is developed to evaluate the latent volatilities of the TSE Index. The data used to estimate the models include the values of the total index of the TSE from the beginning of 2020 to the beginning of 2021 on a daily basis with a frequency of 30 minutes. Also, in order to determine the error, data from the date (03/27/2021) to (12/21/2021) has been used in 15-minute intervals. the square logarithm distribution of returns as a measure of realized volatilities is first simulated using a stochastic volatility model to obtain latent volatilities and then using a mixture of copula family distributions and the MCMC, modeling and estimation were performed in the training phase and finally in the test phase using out-of-sample data to estimate the stochastic volatility of the test phase was investigated. The results show that among the functions of Copula Gumble, Galambos, Joe, Clayton and Frank in the test phase, 3 Copula Gumble, Galambos, Joe have acceptable performance and among these functions, the Gumble-Stochastic Volatility based on MCMC with the lowest error rate among the out-sample data recorded better performance.