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

Abstract: 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.