缺失数据环境下汇率序列的潜变量Metropolis-Hastings算法及触发式理财产品定价  

The Latent Variable Metropolis-Hastings Algorithm for Exchange Rate Series in Case of Missing Data and Pricing the Triggered Financial Products

作　　者：董艳[1] DONG Yan(Department of Basic Science,Shaanxi Railway Institute,Weinan 714000)

机构地区：[1]陕西铁路工程职业技术学院基础部,渭南714000

出　　处：《工程数学学报》2021年第3期330-342,共13页Chinese Journal of Engineering Mathematics

基　　金：陕西铁路工程职业技术学院科研基金(KY2019-42).

摘　　要：金融数据序列的参数估计是现代金融学研究的热点之一,也是数理金融学的一个重要研究方向.在缺失数据情形下,本文采用MCMC方法研究了ARMA汇率序列的参数估计问题.首先,将潜变量插补数据方法融入MCMC采样过程,新的MCMC参数估计方法允许序列存在缺失数据.其次,结合潜变量,获取了自回归系数和白噪声方差的共轭后验分布.再次,由于滑动平均系数的共轭后验分布获取困难,构造了一种基于多元回归的参数估计方法.最后,利用Metropolis-Hastings抽样替代Gibbs抽样并融入上述结果,形成了一种新的MCMC参数估计方法,该方法有效克服了单纯Gibbs抽样序列存在的波动聚集现象的不足.此外,以2018年9月20日至9月27日的欧元兑美元汇率为仿真对象,对触发式理财产品进行了实证分析.Parametric estimation of financial assets is one of the hot topics in modern finance,and also one of the important research fields in mathematical finance.In this paper,the MCMC method is used to study the parameter estimation problem of ARMA exchange rate series in case of missing data.Firstly,the latent variable interpolation method is integrated into the MCMC sampling process.The new MCMC parameter estimation method allows the missing data in the sequence.Secondly,combined with the latent variable,the conjugate posterior distributions of autoregressive coefficients and the white noise variance are obtained.Thirdly,a parameter estimation method based on multiple regression is constructed,due to the difficulty in obtaining the conjugate posterior distributions of moving average coefficients.Finally,using the Metropolis-Hastings sampling instead of Gibbs sampling and incorporating the above results,a new MCMC parameter estimation method is developed.This method effectively overcomes the shortcomings of the volatility aggregation phenomenon of the pure Gibbs sampling sequence.In addition,the euro-dollar exchange rate from September 20 to September 27,2018 is used as the simulation object,and the empirical analysis of triggered wealth management products is carried out.

关 键 词：ARMA汇率序列 触发式理财产品 潜变量Metropolis-Hastings抽样 Bayesian后验 

分 类 号：F830.9[经济管理—金融学] O211.6[理学—概率论与数理统计]