Continuous Time Of Bayesian Model And Empirical Analysis

Model in the financial field can be traced back to the earliest application at the end of the 1960s and early 1970s by Merton (1973), the model was first put forward in the application of dynamic portfolio investment and consumption of stochastic programming. With the develop-ment of 30 years, continuous time method has been widely used in financial engineering and option pricing, derivative term structure of asset pricing and portfolio theory. The paper used the MCMC method to estimate posterior distribution of random fluctuation model. MCMC method can also be used in multivariable models, it don't need accurate parameters of the posterior dis-tribution to simulate parameters from the condition parameters of the posterior distribution.Firstly, the paper introduced the current development and significance of research about the continuous and discrete random fluctuation models. Because the real exchange data are al-ways discrete, the continuous time model should be discrete; the Milstein method is a right way to solve this problem. I adopt the method of MCMC to estimate the parameters of the models, The models were used to describe the stock and currency fluctuations in income volatility and sustainability. Then it got the value of parameters estimation about the model through the Win bugs software due to the computation. it could be found out the likelihood functions and corre-sponding parameters posterior probability density function with Bayesian method. Through applying Bays and MCMC principle for model estimation, it increased the dimension of pa-rameters. It also could be calculated the posterior distribution by using the Bayesian methods. According to the principle of MCMC,the parameters and implied in the posterior distribution variables can be extracted from the posterior sample, then got the parameters and implicit pos-teriori estimation of variables. The next part of paper is about ARCH model, ARCH model is widely known method in financial time series.it was used to estimate and forecaste the ex-change data. Then I compared the two kinds of models through the data anlaysis results and DIC standard.It adopt the dollar/pounds exchange rate data between 01/10/81 and 28/6/85 in emperical analysis.then analyzed the discrete model simulation of the two models, reach out the program-ming model and parameter estimation convergence index. Through the comparison the two kind of models, it found out the stochastic variance model has better fitting degree than ARCH.