SVJD-LIBOR随机动态模型的市场校准估计与实证模拟

针对跳跃扩散LIBOR市场模型（JD-LIBOR）与随机波动率LIBOR市场模型（SVJD-LMM）各自应用局限，首先将正态跳跃扩散与Heston随机波动率同时引入标准化LIBOR市场模型中，建立一类新型双重驱动非标准化LIBOR市场模型（SVJD-LMM）。其次，运用Cap、Swaption等利率衍生产品市场数据和Black逆推校准方法，对模型的局部波动参数与瞬间相关性参数进行有效市场校准；并运用自适应马尔科夫链蒙特卡罗模拟方法（此后简称A-MCMC）对模型的随机波动率、跳跃扩散等其他主要参数进行有效理论估计与实证模拟。最后，针对六月期美元Libor远期利率实际数据，对上述三类市场模型进行了模拟比较分析。研究结论认为，若在单因子Libor利率市场模型基础上引入跳跃扩散过程，并且联立波动率的随机微分方程，则可极大地提高利率模型的解释力；加入随机波动率和跳跃扩散过程的模拟计算结果与实际利率的误差更小，从而更接近现实情况。

Market Calibration Estimation and Empirical Simulation of SVJD-LIBOR Market Models

In view of the application limitation of jump-diffusion Libor market model (JD-LMM) and stochastic -volatility Libor market model (SV-LMM), firstly it introduces the normal jump diffusion and Heston stochastic volatility into the standard Libor market model, and sets up a new dual driving non-standardized Libor market model (SVJD-LMM). Secondly, using interest rate derivative securities market data such as Cap(Caplet) and the Sswaption market volatility,and Black inverse parameters calibrating methods it makes an effective market calibration for some model parameters such as local volatility and instantaneous correlation coefficient . Then, on the basic of adaptive Markov chain Monte Carlo simulation method (MCMC), an effective theory estimation and empirical simulation of other models parameters areis given.. Finally, according to actual data of the six- months US Libor forward rate, it gives an calculation and comparative analysis to the above three models. The research conclusions are: in view of the short-term Libor, compared with LMM and SV-LMM, SVJD-LMM model has less simulation errors and better simulation effect.