LEVY-LIBOR市场模型的蒙特卡罗模拟参数校准与估计

基于远期LIBOR利率的随机波动与无限跳跃特征，针对标准化LIBOR市场模型（LMM）和随机波动率LIBOR市场模型（SV-LMM）应用局限，进一步引入Levy无限跳跃过程，建立多因子非标准化Levy 跳跃随机波动率LIBOR市场模型（SVLEVY-LMM）。在此基础上，基于非参数化相关矩阵假设，运用互换期权（Swaption）、利率上限（Cap）等主要市场校准工具和蒙特卡罗模拟技术，对模型局部波动率和瞬间相关系数等参数进行有效市场校准；应用自适应马尔科夫链蒙特卡罗模拟方法（A-MCMC）对Levy跳跃与随机波动参数进行有效理论估计。实证认为，对远期利率波动率校准，分段固定波动率结构较为符合市场实际情况；对远期利率相关系数矩阵校准，非参数化相关系数矩阵具有最小估计误差和最佳的市场适应性；SVLEVY-LMM能够最好拟合远期LIBOR利率。

Parameter Calibration and Estimation of Levy-LIBOR Market Models Based on Monte Carlo Simulation

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.