The Continuous-Time Stochastic Volatility Models And Application In Chinese Stock Market

The continuous-time models can be applied a lot when studying finance. In the financial market, the volatility and the risk is becoming larger and larger along with the development of the financial market at home and abroad. Now studying the economic meaning, inherent mechanism and characteristic of the financial volatility are important. This dissertation mainly studies and discusses the continuous-time stochastic volatility models with jumps.The dissertation discusses the methods for discretizing and estimating continuous-time models. There are two methods for discretization: Euler discretization and Milstein discretization. We mainly studies the method which is efficient and easy for estimating continuous-time models—Markov Chain Monte Carlo (MCMC). And programming in R to estimate the continuous-time stochastic volatility model with jumps using MCMC. It is helpful to make the results more accurate compared with estimating the model by some software.The dissertation analyses Chinese stock market using the continuous-time stochastic volatility models with jumps in returns and volatilities. Estimating the model by MCMC and taking two examples based on Shanghai Stock Exchange index. The results show that the volatilities and jumps in Chinese stock market now becomes small.The continuous-time stochastic volatility models are usually applied in the finance derivative pricing, interest rate term structure, asset pricing and so on. This dissertation applies them to forecast the Stock Exchange index in the future. The empirical results show that the data simulated by the continuous-time stochastic volatility model is close to the real data and we could use these models to forecast the volatilities and jumps in the stock market in order to avoid risks.