The Research On The Market Calibration And Parameter Estimation Methods For Stochastic Volatility Levy-LIBOR Dynamic Model

With the development of the liberalization of the interest rate market and the promotion of RMB internationalization strategy, interest rate derivatives will boom in the domestic financial market in the near future. What’s more, we are working to develop the SHIBOR rate as benchmark interest rate in the money market in China.Because there are underlying similarities between SHIBOR and LIBOR rate, the study of LIBOR product pricing and risk management will contribute to the development of SHIBOR. Therefore, effective modeling of long-term rate’s stochastic process becomes an important theory and practical issue which deserves research.Nowadays, the standard LIBOR market model is widely used to model the rate’s stochastic process. But the standard LIBOR market model shows a lot of deficiencies. There will be a lot improvement in the extensions of the standard model,market calibration methods and parameter estimation methods to make it better predict dynamic characteristics of forward rates.This paper starts from the expanded LIBOR dynamic model and achieves precise description of forward LIBOR rates by improvement of market calibration methods and Monte Carlo method of parameter estimation. All parts of the structure and contents are as follows:First, we illustrate the background of research issues, overall framework of research and innovation of this paper. And we review the existing literature and are inspired by LIBOR market model with stochastic volatility and levy jump process.Secondly,we propose the stochastic volatility Levy-LIBOR dynamic model. We derive the standard LIBOR market model by the definition of forward interest rate.Then the stochastic differential equations based on LIBOR model is built to describe the interest rate derivatives. Finally, we analyze the characteristics of stochastic volatility and jumps of forward rates and derive stochastic volatility Levy LIBOR market model.Third, we study the calibration methods of the LIBOR market model. Two common calibration tools interest-rate cap and swaption are introduced in the first place. Then traditional parametric methods and one new non-parametric method are used to calibrate model’s instantaneous correlation matrix respectively.Fourth, we propose the parallel adaptive Markov Chain Monte Carlo method to estimate parameters. We employ a parallel adaptive Metropolis-Hastings sampling algorithm to improve the convergence efficiency. Then the new Adaptive Markov Chain Monte Carlo method is used to estimate different Levy-LIBOR market model parameters and compared with normal one. In the end different paths of forward LIBOR rates are simulated and analyzed.Finally, we summarize the aforementioned theoretical and empirical analysis of the content and prospects for future research directions.By reading literature at home and abroad, coupled with theoretical studies and empirical analysis, we can draw the following conclusions:First, empirical results that Levy jump stochastic volatility LIBOR model can more accurately describe the forward rate dynamic trend than standard LIBOR market model and stochastic volatility LIBOR market model. Compared with finite jump process such as compound Poisson jump process, infinite Levy jump process better simulate the dynamic characteristics of forward LIBOR rate. Secondly, on long-term interest rate volatility calibration, segment-fixed structure is in line with market conditions. And for the calibration of correlation coefficient matrix, the non-parametric Monte Carlo method could get the minimum estimation error and the best market adaptability. Finally, we use the parallel adaptive MCMC method to estimate stochastic volatility and Levy jump process parameters and demonstrate that this method could achieve higher convergence efficiency than ordinary one.