基于机制转换特征与随机波动率Libor市场模型（此后记为SRSV-LMM），利用傅里叶分析和费曼-卡茨定理，对CMS价差期权（CMSSO）价格的理论计算问题进行深入分析与探讨.首先，针对CMS价差期权的内涵特征及其价值组成，提出该类产品定价的理论计算框架；其次，基于标的Libor利率与互换利率的随机与阶段变化特征，建立具有随机波动率和机制转换性质的Libor市场模型以及互换利率市场模型（此后记为SRSV-SMM），并运用Black逆推公式和自适应马尔可夫链蒙特卡罗模拟方法（此后记为MCMC）对该模型进行有效参数市场校准与模拟估计；最后，基于SRSV-LMM和SRSV-SMM模型假设，利用费曼-卡茨定理和傅里叶逆变换方法得出CMS价差期权的理论计算公式，并通过实例进行实证计算与比较分析.研究结论认为，对远期Libor利率与互换利率生成路径的蒙特卡罗模拟来说，SRSV-LMM、SRSV-SMM具有更优越拟合效果；与蒙特卡罗模拟方法比较，本文提出CMS价差期权理论定价公式在价格计算时间与实际数据利差上体现出更好的实证效果.
Abstract
Based on LMM with switching regime and stochastic volatility, theoretical methods on CMSSO are deeply analysized and explored by mean of Fourier analysis and Feynman-Katz theorem. Firstly, according to the connotation feature and value composition of CMSSO, we put forward a theoretical computational framework for pricing this product. Secondly, basing on the random and switching jump features of Libor and Swap rates, we set up LMM/SMM with stochastic volatility and switching regime, and make an effective calibration and estimation for models parameters by using Black-backstepping and adaptive MCMC. Lastly, on the basic of SRSV-LMM and SRSV-SMM, the theoretical computational formulas are given, and their empirical computation and comparative analysis are made by means of Fourier analysis and Feynman-Katz theorem. The research conclusion is:according to the Monte Carlo simulation result of forward Libor and Swap rates paths, SRSV-LMM、SRSV-SMM have less simulation errors and better simulation effect. Further, compared with Monte Carlo method, our methods reflect better empirical result basing on computation time and simulation accuracy.
关键词
机制转换 /
随机波动率 /
Libor市场模型 /
CMS价差期权 /
傅里叶分析
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Key words
switching regime /
stochastic volatility /
Libor market models /
CMS spread option /
Fourier analysis
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中图分类号：
F830.91
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基金
国家自然科学基金（71271190）；教育部人文社会科学研究项目（15YJA630037）
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