Modeling Stock Return Volatility Using Symmetric and Asymmetric Nonlinear State Space Models: Case of Tehran Stock Market

Volatility is a measure of uncertainty that plays a central role in financial theory, risk management, and pricing authority. Turbulence is the conditional variance of changes in asset prices that is not directly observable and is considered a hidden variable that is indirectly calculated using some approximations. To do this, two general approaches are presented in the literature of financial economics for modeling and calculating volatility. In the first approach, conditional variance is modeled as a function of the square of the past shocks of return on assets. Models of the GARCH type fall into this category. In the alternative approach, volatility is assumed to be a random variable, which evolves using nonlinear patterns of Gaussian state space. This type of model is known as Stochastic Volatility (SV).  Because, SV models include two kinds of noise processes, one for observations and another for hidden, volatility, thus, they are more realistic and more flexible in calculating volatility than GARCH type.  This study attempts to analyze the volatility in stock returns of 50 companies, which are active in Tehran Stock Market using symmetric and asymmetric methods of Stochastic Volatility, which is different in the presence of leverage effect. The empirical comparison of these two models by calculating the posterior probability of accuracy of each model using the MCMC Bayesian method represents a significant advantage of the ASV model. The results in both symmetric and asymmetric methods represent the very high stability of the volatility generated by the shocks on stock returns; therefore, the Tehran Stock market changes in returns due to this high sustainability will be predictable.