Research On Correlation Coefficient Estimation And Option Pricing Method Based On Monte Carlo Method

In recent years,with the development and advancement of science and technology,computers have been widely used in various fields.In mathematics,with the acceleration of computer speed,computational mathematics has made new breakthroughs and added many new contents.Monte Carlo method is an important part of it.The emergence of the Monte Carlo method has promoted the development of research and opened up a new direction for people to solve problems.In this paper we study the European option pricing based on Markov chain Monte Carlo method and GARCH model and use the simulated annealing algorithm to improve the boundary of Kendall rank correlation coefficient and Spearman rank correlation coefficient.This paper has four chapters,arranged as follows:In chapter 1,we briefly introduce the significance the application field and the current situation of Monte Carlo.In Chapter 2,we introduce the Markov Chain Monte Carlo method.In Chapter3,we use the the simulated annealing algorithm to determine the boundary between the Kendall rank correlation coefficient and the Spearman rank correlation coefficient,and get the Copula probability density function corresponding to this boundary.In chapter4,we study the price of the European option by combining the Markov chain Monte Carlo method with the GARCH model.The GARCH model of the Markov chain Monte Carlo method is performed by using the data of the S&P 100 European Index option.After empirical analysis,it was found that the improved model has a certain degree of improvement in the accuracy of European option pricing.In chapter5,we summarize the main work of this paper,expound the research content and the results obtained,and look forward to the future research direction...