A Study On Stochastic Volatility Models And Forecasting Of Volatility

In 1952, Markowitz introduced the standard deviation to do the measurement of the portfolio risk in the CAPM, this historical creation help people to measure the risk of financial assets quantitatively. Subsequently, the study of the financial property’s volatilityis mainly focused on the Mean reversion phenomena and Volatility clustering. There exist two kind of model modeling the volatility, one is the Garch model, which assume that the future volatility is a linear function of historical volatility and historical yields square; the other is the stochastic volatility model, which assume that the volatility sequence are random sequence, and returns process is a Wiener process.The volatility of financial asset returns own some features, there are thick tails, leverage effect, volatility clustering, mean reversion, jump and so on. According to the prior research, because there are correlations between the yields, it is difficult in modeling the leverage and fat-tail effectin one model together. Therefore, the article proposed a new stochastic volatility model considering fat-tail(T-distribution) and leverage effect, it is called ASV-T model. Moreover, the article adding a skip factor to the new ASV-T model in order to characterize the jumping features of financial assets.The stochastic volatility model we discussed describes the leverage effect, thick tails, and jump features of the financial assets. First, we made statistic analysis of the model, made Bayesian statistical distribution parameter estimation anddescribed the procedure of Gibbs sampling. Second, we propose the means to predict the volatility using the ASV-TJ model. Third, we compare the jump features reflecting in the GEM market and in the NASDAQ market. Finally, we use the ASV-TJ, the ASV-T, and the SV-T model to predict the volatility in the GEM market, calculating the MSE loss function and the QLIKE loss function of each model, and use the D-M statistics to check each model’s performance.The results confirm that: these years, the China’s GEM market reflects obvious persistent volatility, leverage, thick tail and jumping phenomenon. When predict the volatility of the GEM market, we find that the ASV-TJ model is the best among the three models, and the ASV-T model is better than the SV-N model. What is more, we find the jumps in frequency and volatility levels of the GEM market are higher than those of the NASDAQ.