The Application Of Markov Chain Monte Carlo Method In The Parameter Estimation In Financial Models

The dynamics of the variables (such as the stock price,interests,etc.) are paid closeattention to in the financial markets. Scholars have set up financial models to describetheir dynamics. The Cox-Ingersoll-Ross model, which helps to describe the dynamicsof the interests, is one.As the financial models have played important roles in revealingthe dynamics of the variables, the parameter estimation is of great significance.Bayesian estimation is one of the useful ways of estimating parameters. Usually,theparameters, considered as stochastic variables, are estimated by the expectations of theposterior distribution. The posterior distribution can be calculated by the priordistributions and the likelihood function. When the calculation of the expectations isdifficult, the Monte Carlo simulation can be used instead. But when it is difficult tosample from the Monte Carlo simulation, the Markov Chain Monte Carlo (MCMC)method is of great help. MCMC method utilizes the convergence’s property of anaperiodic,irreducible Markov Chain. So with a proper transition density, a MarkovChain converging to the desired distribution can be constructed. Then after enoughtimes of transitions, the correlated samples from the chain can be considered as tofollow the desired marginal distribution. Taking the Cox-Ingersoll-Ross model as anexample, this paper reviews and discusses several key points in MCMC method, suchas choosing the proposal transition density and the accept-refuse algorithm, thecalculation of the variance, the analysis of the convergence, etc, selects or adjustsappropriate methods, and utilizes the MCMC method to estimate the parameters of theCox-Ingersoll-Ross model based on the SHIBOR (overnight) between Oct8,2006toOct21,2013. The result is good, indicating that it is applicable to use MCMC methodin estimating parameters in the financial models.