SABR随机波动率LIBOR市场模型的参数校准估计方法与实证模拟

针对标准化Libor市场模型（LMM）和Heston随机波动率Libor市场模型（Heston-LMM）的应用局限，首先将SABR代替Heston过程引入标准化Libor市场模型框架，建立非标准化的SABR随机波动率Libor市场模型（SABR-LMM）；在此基础上，运用利率上限期权（Cap）、利率互换期权（Swaption）和自适应马尔科夫链蒙特卡罗模拟方法（MCMC）对模型参数进行有效市场校准与模拟估计；最后，针对三个月美元Libor远期利率实际数据，对上述三类Libor市场模型的实际运行效果进行了实证模拟计算与比较分析。研究结论认为，基于模拟利差计算结果，针对短期Libor利率模拟而言，与LMM和Heston -LMM两类模型而言，加入SABR波动项的SABR-LMM模型具有更小的模拟误差，因而具有更好的模拟效果。

Market Calibration and Estimation on Parameters and Empirical Simulation for SABR-LMM

Based on the limitation of application for the standard Libor market model (LMM) and Heston stochastic volatility model Libor market (HESTON-LMM), it sets up a non-standardized Libor market model with SABR stochastic volatility (SABR-LMM) by using Heston process and introducing SABR Stochastic volatility into the standard Libor market model. Secondly, according to Cap(Caplet) , the swap market volatility, as well as the adaptive Markov chain Monte Carlo simulation method (MCMC), it makes an effective calibration and simulation for modes parameter. Finally, according to actual data of the six- months US Libor forward rate, it gives an empirical simulation calculation and comparative analysis to above three models. The research conclusions are: in view of the short-term Libor, the SVJD-LMM has less simulation errors and better simulation effect comparing with LMM with Heston volatility term and LMM.