机器学习下混合分数Vasicek模型的校准  

Calibration of the mixed fractional Vasicek model based on machine learning

作　　者：陈树国 王冬法 朱海军 邓明荣[3] 马弘 CHEN Shuguo;WANG Dongfa;ZHU Haijun;DENG Mingrong;MA Hong(State Grid Zhejiang Electric Power CO.,LTD.Hangzhou 310007,China;State Grid Zhejiang Procurement Company,Hangzhou 310007,China;School of Management,Zhejiang University,Hangzhou 310058,China)

机构地区：[1]国网浙江省电力有限公司,浙江杭州310007 [2]国网浙江省电力有限公司物资分公司,浙江杭州310007 [3]浙江大学管理学院,浙江杭州310058

出　　处：《管理工程学报》2021年第3期241-249,共9页Journal of Industrial Engineering and Engineering Management

摘　　要：基于机器学习中的回归方法,结合零息票债券的价格,研究风险中性测度下混合分数Vasicek模型的参数估计与预测问题。首先利用混合分数布朗运动的随机积分理论,得到混合分数Vasicek利率模型下零息票债券的定价模型。然后,利用对数零息票债券价值的正态性以及高斯过程的机器学习回归法,给出了由零息票价格求得混合分数Vasicek模型未知参数的估计量,并给出了预测方法。最后,采用蒙特卡洛模拟说明了方法的可行性和可靠性。In this era of“big data”,we usually apply techniques such as parameter estimation,structural estimation and state-of-theart machine learning algorithms on managing and making decisions.This calls for a deep understanding of practical and theoretical aspects of methods and models from statistics,econometrics and computer science,combined with relevant domain knowledge.Machine learning in financial engineering has become more prominent recently due to the availability of vast amounts of data and more affordable computing power.Calibration of interest rate models under the risk-neutral measure typically entails the availability of some derivatives such as swaps and caps.This paper considers the problem of calibration of the mixed fractional Vasicek model based on machine learning.Using the conditional expectation for the mixed fractional Vasicek model,we obtain the pricing model for zero coupon bond.The calibration is done by maximizing the likelihood of zero coupon bond log prices,using mean and covariance functions computed analytically,as well as likelihood derivatives with respect to the parameters.The maximization method used is the conjugate gradients.The only prices needed for calibration are zero coupon bond prices and the parameters are directly obtained under the neutral measurement of free arbitrage risk.In the first part,using the stochastic integration for mixed fractional Brownian motion,this paper proposes an analytical solution for the mixed fractional Vasicek model.Using the conditional expectation for the mixed fractional Vasicek model and partial differential equation,this paper proposes the pricing model for the zero coupon bond.Under the mixed fractional Vasicek interest rate model,the risk-neutral zero coupon bond prices follow a log-normal distribution,which can easily be transformed into a Gaussian process by taking the logarithm of the zero coupon prices.The mean and covariance functions of this Gaussian process can be computed analytically making it suitable for Gaussian processes for m

关 键 词：混合分数Vasicek过程 机器学习 零息票债券 极大似然估计 贝叶斯估计 

分 类 号：F830.59[经济管理—金融学]