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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.
Based on the mechanism transformation feature and the stochastic volatility Libor market model (hereinafter referred to as SRSV-LMM), the theoretical calculation of the price of CMS spread (CMSSO) is analyzed and discussed by means of Fourier analysis and Feynman-Katz theorem First of all, aiming at the connotation characteristics and its value composition of CMS spread options, a theoretical framework for pricing such products is proposed.Secondly, based on the stochastic and phase change characteristics of the underlying Libor interest rates and swap rates, Nature of the Libor market model and the exchange rate market model (hereinafter referred to as SRSV-SMM), and using the Black inverse formula and adaptive Markov chain Monte Carlo simulation method (hereinafter referred to as MCMC) the effective parameters of the model Market calibration and simulation estimation. Finally, based on the assumption of SRSV-LMM and SRSV-SMM model, the theoretical calculation formulas of CMS spread options are obtained by using the Feynman-Katz theorem and the inverse Fourier transform method. The empirical calculation and The conclusion is that the SRSV-LMM and SRSV-SMM have a better fitting effect for the Monte Carlo simulation of long-term Libor interest rate and swap rate generation paths; Compared with the Tekaro simulation method, this paper proposes that the pricing formula of CMS spread option theory shows a better empirical result on the price calculation time and the actual data spread.