SRSV-LMM模型的校准估计与CMS差价期权定价

发布时间：2018-01-12 19:17

本文关键词：SRSV-LMM模型的校准估计与CMS差价期权定价　出处：《系统工程理论与实践》2017年02期 　论文类型：期刊论文

【摘要】：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 the characteristics of mechanism transformation and stochastic volatility Libor market model (the postscript is SRSV-LMMN), Fourier analysis and Ferman-Katz theorem are used. In this paper, the theoretical calculation of CMS spread option is analyzed and discussed. Firstly, the connotation characteristics and value composition of CMS price difference option are analyzed and discussed. The theoretical calculation framework of pricing of this kind of products is put forward. Secondly, based on the stochastic and phase characteristics of the underlying Libor interest rate and the swap interest rate. The Libor market model and the swap interest rate market model (SRSV-SMMM) with stochastic volatility and mechanism transformation are established. Using Black inverse formula and adaptive Markov chain Monte Carlo simulation method, the effective parameter market calibration and simulation estimation of the model are carried out. Finally, based on the assumption of SRSV-LMM and SRSV-SMM model, the theoretical formula of CMS spread option is obtained by using Feynman-Katz theorem and inverse Fourier transform method. The conclusion is that SRSV-LMM can be used to simulate the generation path of forward Libor interest rate and swap interest rate. SRSV-SMM has better fitting effect. Compared with the Monte Carlo simulation method, this paper proposes that the pricing formula of CMS's spread option theory shows a better empirical effect on the difference between the price calculation time and the actual data interest rate.
【作者单位】：浙江大学城市学院;浙江财经大学;
【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)~~
【分类号】：F830.9
【正文快照】： 1引言基于金融管制放宽及商品多样化需求,利率衍生品市场取得了迅速发展.根据国际清算银行(BIS)统计,2013年末利率衍生品合约名义本金相比2000年增长7.21倍,在全球衍生品市场的比重达78.94%.在所有利率衍生品之中,尤其以CMS类利率衍生产品受到更为广泛关注.由于CMS类产品价值

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