Research On The Genetic Optimization Algorithm Parameter Estimation Method For Stochastic Volatility CGMY-LIBOR Dynamic Model

The LIBOR rate is playing the important role of benchmark interest rate of the international financial market,the accuracy of modeling a stochastic process which LIBOR interest rate obeys become the premise and the key factor of the interest rate derivatives pricing.In financial market,the standard LIBOR market model is basically chosen when modeling the stochastic process of LIBOR.However,the standard market model assumes that the implied volatility is constant,but actually implied volatility has the characteristics of volatility smile or deflection,so that makes the distribution of logarithmic LIBOR rate following the normal distribution of the left fat tail or the peak thick tail and this defect is particularly important for the pricing of interest rate derivatives.If you can’t accurately reflect volatility skew or smile characteristics existing in the financial markets,it is likely to lead to serious pricing error,resulting in serious economic loss.Therefore,it is very important to improve the existing standard LIBOR market model to better fit the dynamic change characteristics of forward rate.With the advancement in marketization of our country interest rate,the domestic interest rate derivatives innovate constantly.Nowadays,our country is pushing the SHIBOR interest rate as the benchmark interest rate in China’s monetary market in our country,so the expansion research of the LIBOR market model has important reference to SHIBOR rate derivatives pricing in our country.In this paper,we start from the extended LIBOR stochastic model,and try to introduce the CGMY jump process into the model to establish the CGMY-LIBOR stochastic volatility model.At the same time,we try to use the genetic optimization algorithm learning from the law of evolutionary biology(including the rules of survival of the fittest,genetic mutation,hybridization,etc.)to estimate the parameters and the parameters in the model are estimated as gene fragment to be selected,crossed,mutated.The content of this paper is mainly divided into the following parts:Firstly,we elaborate the research background of this article and the overall framework and innovations.Secondly,we review and summary the existing literature at home and abroad,which leads to the establishment of the model.Thirdly,we first introduce stochastic interest rate model and stochastic volatility.Subsequently,we introduce the related concept definition of the Levy process.Then we make the the brief analysis of the standardized model,LIBOR stochastic volatility model and Levy stochastic volatility model.Finally,from the standpoint of the brief analysis of the stochastic interest rate and Levy process,we establish the random fluctuations CGMY-LIBOR market model.Fourthly,the existing model parameters estimation methods are summarized and genetic optimization algorithm based on the model is proposed,and then the preliminary knowledge of genetic optimization algorithm is introduced to estimate the parameters.Finally,the genetic optimization algorithm is used to estimate the parameters.Fifthly,first of all,the data is selected and processed,then the difference between MCMC and genetic optimization algorithm is introduced,and the model parameters are estimated by genetic optimization algorithm.Finally,we make conclusions and research prospects.We summarize the theoretical derivation and empirical analysis of this paper,and the future research directions are prospected.By summarizing and combing the literature at home and abroad with the theoretical and empirical research,this paper can get the following conclusions:First,the stochastic volatility process and the CGMY process which are introduced into the standard LIBOR market model can theoretically describe the LIBOR interest randomness and jump characteristics more accurately.Second,the empirical results show that the application of genetic optimization algorithm to estimate the model parameters in this paper can search the global optimal solution,and have a higher convergence efficiency,besides,CGMY-LIBOR stochastic volatility market model can more accurately describe the long-term trend of LIBOR interest rate changes.