基于MCMC模型的利率随机波动率分析  

Stochastic volatility analysis of interest rate based on MCMC model

作　　者：韩琦 夏鑫洲 HAN Qi;XIA Xinzhou(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报(理学版)》2025年第3期33-40,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(62261049,12261080);甘肃省自然科学基金资助项目(20JR10RA085);甘肃省教育厅高等教育创新基金资助项目(2022A-017)。

摘　　要：目前关于利率波动率指数的研究是在利率衍生品价格模型的基础上构造的,为了进一步扩展利率隐含波动率指数的应用范围,在利率波动模型的基础上研究收益率数据信息中隐含的随机波动率的性质。基于2021年1月至2023年2月的国债收益率数据,通过马尔可夫链蒙特卡罗(Markov chain Monte Carlo,MCMC)模型对收益率数据进行建模分析。结果表明:在收益率为基础的利率波动率模型中,长期利率的波动性明显低于短期利率的。本文使用国债收益率作为基础数据,相较于期权市场中的波动率指数,本文的模型不受期权市场上期权种类以及规模的影响,具有更大的适用范围。Currently,researches on the interest rate volatility index are constructed on the basis of the interest rate derivative price model.To further expand the application scope of the implied interest rate volatility index,the properties of the stochastic volatility implied in the yield data information are studied on the basis of the interest rate volatility model.Based on the yield data of government bonds from January 2021 to February 2023,the yield data are modeled and analyzed by the Markov chain Monte Carlo(MCMC)model.The results show that the volatility of the long-term interest rate is significantly lower than that of the short-term interest rate.Because this paper uses the treasury bond yield as the basic data,compared with the volatility index in the option market,the model in this paper is not affected by the type and scale of options in the option market and has a greater range of application.

关 键 词：利率模型 随机波动率 马尔可夫链蒙特卡罗模型 波动率指数 

分 类 号：O29[理学—应用数学] F222.1[理学—数学]