Modeling Historical Volatility of 10-year Chinese Treasury Bond Futures: A Comparative Analysis of MLE and MCMC Approaches

Abstract

Chinese treasury bond futures are gaining significance in the market. Volatility is an important metric for measuring the fluctuations in asset prices. This paper provides historical volatility modeling for 10-year Chinese treasury bond futures through the Student-t distribution GARCH (1,1) model. The data encompasses the entire historical daily prices, which are used for calculating logarithmic returns. Before modeling, plots and hypothesis tests such as Augmented Dickey-Fuller testing and Lagrange Multiplier testing, are performed to assess the underlying assumptions. In pursuit of better outcomes, a comparative analysis is conducted on parameter estimation, by using both the Maximum Likelihood Estimator (MLE) and Markov Chain Monte Carlo (MCMC) with the Metropolis-Hasting algorithm. The results are performed by “fGarch” and “bayesGARCH” packages in RStudio. Two methods give different estimates, but both accurately fit the dataset. The forecast errors show the MLE is better. However, a generalizable conclusion remains elusive, primarily due to disparities in data sources, model configurations, and the default settings in R packages.