Bayes Analysis Of Continuous-Time Assets Return Models

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. Bayes theory was used to analyze Continuous-time models. The key points and main achievements of this work are listed as follows:1)The parameters of Continuous-time models were estimated using Markov chain Monte Carlo method (MCMC). The method is based on Markov-chain Monte Carlo methodology and applies to a wide class of models including systems with unobservable state variables and nonlinearities. In the paper, The method is applied to the estimation of parameters in Double Exponential Jump Diffusion Model(DEJD).2)The Continuous-time structural change models were studied. The method for detecting and locating single structural change point using MCMC method is proposed. The method for detecting and locating multiple structural change points of continuous time models is also put forward. The method suggested is proved to be effective and feasible by theoretical analysis as well as the structural change analysis the distribution of the return series of composite index of Shanghai stock markets.3)The Hyperbolic Jump-Diffusion model was put forward. Based on Bibby and Sorensen's Hyperbolic Diffusion model(HYD), we model the log-price as a deterministic linear trend and jumps plus a diffusion process with drift zero and with a diffusion coefficient (volatility) which depends in a particular way on the instantaneous asset price. We name the model Hyperbolic Jump-Diffusion model(HJD). It is shown that the model possesses a number of properties encountered in empirical studies of asset prices. The model is rather successfully fitted to different price index data sets. We proposed a MCMC method to estimation parameters and implied variables, the MCMC method based on the Milstein scheme.4)The likelihood ratio test based on stochastic simulation was used to compare standard BS model with structural change BS model. With this method we compare the goodness of fit betwen HYD and HJD models.The research is sponsored by National Natural Science Foundation of China: Bayes Analysis of Continuous-time Models (No. 70301006) and Research on Long Run Eqilibrium in Multivariate Moments Series and Avoiding Tactics of Dynamic Financial Risk (No. 70471050).