Residual Analysis of Financial Models for Stock Indices using MCMC

Abstract

In this paper I have analyzed four different markets: KOSPI, S&P500, NIKKEI225 and HANGSENG. In order to estimate the models with stochastic volatility and Merton’s jump, which have yet not known their density function in closed form, I have developed Bayesian Markov chain Monte Carlo (MCMC) methods using discretely sampled data. Simulation studies show that jumps and volatility are not compatible each other. Empirical studies show that there is an appropriate model for each market but Log-Stochastic model showed the best performance. If there is a crisis during analysis period, there is a significant change in the parameters of its model.