Research On Random Wave Model With Jump Based On MCMC Method

Volatility is the key variables of investment portfolio, the capital asset pricing and risk management theory, and is a core issue of research on the financial markets. Financial time series usually exhibits a large fat tail phenomenon, and the result of the volatility described by the basic stochastic volatility model is usually unsatisfactory/In this paper, we conduct research the stochastic volatility model with jumps and stochastic volatility model with fat-tails and jumps.Bayesian method is more efficient on solving the high-dimensional parameter estimation. Therefore, we first apply the Bayesian method to derive the posterior distribution of the parameters of stochastic volatility model with jumps, then implement Monte Carlo simulation of Stochastic volatility model with jumps, and use Markov Chain Monte Carlo methods to estimate the parameters of the model. The results show that MCMC methods have a good effect on estimating the parameters and state variables of the stochastic volatility model with jumps. Using future return price of natural gas of NYMEX from January 2,2007 to February 25,2016, we make empirical research of stochastic volatility model with fat-tails and jumps and stochastic volatility models with jumps. The two models can analyze the volatility of return rate, and stochastic volatility model with fat-tails and jumps can be better to identify the volatility when the financial risks happen.