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

Authors

  • Shujun Zhao

DOI:

https://doi.org/10.54097/gm216756

Keywords:

10-year Chinese Treasury Bond Futures; Historical Volatility; GARCH (1,1) Model; MLE; MCMC M-H Algorithm.

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.

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References

Tang, D, Yang, Y., Yu, Y. Price discovery and volatility spillover effect in treasury bond futures and spot markets: evidence from China. In: IOP Conference Series: Materials Science and Engineering. IOP Publishing, 2018, 32-56.

Ruan, Q., Zhou, M., Yin, L., Lv, D. Hedging effectiveness of Chinese Treasury bond futures: New evidence based on nonlinear analysis. Physica A: Statistical Mechanics and its Applications, 2021, 565: 125553.

Cao, X., Chen, R., Li, Y. Annual Report on the Operation of the Treasury Futures Market in 2022. China Bond (02), 2023, 73-77.

Andersen, T. G., Bollerslev, T., Christoffersen, P. F., & Diebold, F. X. Volatility and correlation forecasting. Handbook of economic forecasting, 2006, 1: 777-878.

Mandelbrot, B. B. The variation of certain speculative prices. Springer New York, 1997, 371-418.

Engle, R. F. Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation. Econometrica, 1982, 50(4): 987–1007.

Bollerslev, T. Generalized autoregressive conditional heteroskedasticity. Journal of econometrics, 1986, 31(3): 307-327.

Nelson, D. B. Conditional heteroskedasticity in asset returns: A new approach. Econometrica: Journal of the econometric society, 1991, 347-370.

Glosten, L. R., R. Jagannathan, and D. E. Runkle. On the relation between the expected value and the volatility of the nominal excess return on stocks. The journal of finance, 1993, 48(5): 1779-1801.

Ding, Z.; Granger, C.; Engle, R. A long memory property of stock returns and a new model. Journal of Empirical Finance, 1993, 1(1): 83-106.

Zakoian, J. M. Threshold heteroskedastic models. Journal of Economic Dynamics and control, 1994, 18(5): 931-955.

Gao, R., Lu, J. An Empirical Study of Soybean Futures Market Correlation Under China-US Trade Frictions: A Copula-GARCH Model Approach. Journal of Sichuan University of Light and Chemical Industry (Natural Science Edition), 2021.

Djeddour-Djaballah, K., & Kerar, L. Quasi-maximum likelihood estimation of GARCH with student distributed noise. Communications in Statistics-Simulation and Computation,2021, 50(5): 1249-1271.

Shiferaw, Y. A. An analysis of East African tea crop prices using the MCMC approach to estimate volatility and forecast the in-sample value-at-risk. Scientific African, 2023, 19: e01442.

Livingston Jr, G. C., & Nur, D. Bayesian inference of multivariate-GARCH-BEKK models. Statistical Papers, 2022, 1-26.

Miskolczi, P. Note on simple and logarithmic return. Applied Studies in Agribusiness and Commerce, 2017, 11(1-2): 127-136.

Hansen, P. R., & Lunde, A. A forecast comparison of volatility models: does anything beat a GARCH (1, 1)?. Journal of applied econometrics, 2005, 20(7): 873-889.

Wuertz, D., RUnit, S., & Chalabi, M. Y. Package ‘fGarch’. Technical report, working paper/manual, 09.11. 2009.

Hastings, W. K. Monte Carlo sampling methods using Markov chains and their applications, 1970.

Ardia, D., & Hoogerheide, L. F. Bayesian estimation of the GARCH (1, 1) model with student-t innovations. The R Journal, 2010, 2(2): 41-47.

Gu, J. M-H Estimation of the GARCH (1,1) Model and Its Applications. Statistics and Decision, 2011, 01: 16-18.

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Published

29-03-2024

How to Cite

Zhao, S. (2024). Modeling Historical Volatility of 10-year Chinese Treasury Bond Futures: A Comparative Analysis of MLE and MCMC Approaches. Highlights in Science, Engineering and Technology, 88, 738-746. https://doi.org/10.54097/gm216756