关键词: 非标准LIBOR市场模型, levy无限跳跃, 市场校准, 互换期权, 蒙特卡罗模拟

Abstract: Nowadays, the standard LIBOR market model(LMM) is widely used to model the rate's stochastic process. But LMM shows much deficiencies. There will be a lot of improvement in the extensions of the standard model to make it better predict dynamic characteristics of forward rates. Based on analysis framework and applicable limitation of LMM with stochastic volatility (SV-LMM), furtherly, the Levy jump process is and intorduced, one kind of new multiple factor non standardized Libor market model (Levy-SVLMM) is set up in. Firstly, this paper calibration methods of the LIBOR market model are studied. 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. Thirdly, the parallel adaptive Markov Chain Monte Carlo method is employed to estimate parameters, and a parallel adaptive Metropolis-Hastings sampling algorithm is employed to improve the convergence efficiency. Lastly, the new Adaptive Markov Chain Monte Carlo method is used to estimate different Levy-LIBOR market model parameters and compared with normal one and the different paths of forward LIBOR rates are simulated and analysied.The empirical research conclusions are: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. 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.

Key words: non-standardized LIBOR market model, Levy jump diffusion, market calibration, swaptions, monte carlo simulation