Compute The VaR Of The Stock Index Based On MCMC Algorithm

Risk measurement is the core and foundation of risk management. With the development of the financial markets, dynamic nature and complexity increase, financial market risk measurement technology becomes more and more comprehensive and complicated. At present, the main methods of financial market risk measurement are sensitivity analysis, volatility, VaR, stress testing, as well as the extreme value theory (EVT). Among them, VaR is the mainstream of the current financial market risk measurement method.Calculate VaR methods are mainly three types:historical simulation, analysis and Monte Carlo simulation method. These three methods have their pros and cons. Historical simulation method is fast, simple and easy to implement and understand。 The calculation process, however, is dependent on a large number of historical data, it is difficult to meet the changing needs of the market. Analysis to collect data and calculations are simple and easy to implement, but market volatility will generate the error, whitch makes it can not effectively test the validity of the function distribution. Monte Carlo simulation method, a high degree of accuracy, can better handle nonlinear problems, but there are still a lack of high-dimensional and static.In1953, Metropolis, Rosenbluth and Teller first proposed MCMC method. In1970, Hastings improved the asymmetric Markov chain, to promote the development of MCMC methods. MCMC methods in statistical physics first discovered and achieved rapid development, has also been widely used in other areas, not just different areas of research focus. For example, in the field of computer science, its focus is to adapt computing scale with the scale of the problem of the growth. With the needs of the application, the method appeared new problems to be solved. In1996Propp and Wilson, as well as in1998Fill promote the development of the idea. Recently, based on the laws of heredity bionics, physics MCMC method gradually begin using the innovation and the use of weighted MCMC recent progress.There are three main MCMC methods:Metropolis-Hastings, Gibbs sampling, plaid Gibbs sampling. This paper will detail the principles and steps, and through the actual example to analysis and proof.