A common factor of stochastic volatilities between oil and commodity prices

ABSTRACT

This article analyses the multivariate stochastic volatilities (SVs) with a common factor influencing volatilities in the prices of crude oil and agricultural commodities, used for both biofuel and nonbiofuel purposes. Modelling the volatility is crucial because the volatility is an important variable for asset allocation, risk management and derivative pricing. We develop a SV model comprising a latent common volatility factor with two asymptotic regimes with a smooth transition between them. In contrast to conventional volatility models, SVs are generated by the logistic transformation of latent factors, which comprise two components: the common volatility factor and an idiosyncratic component. We present a SV model with a common factor for oil, corn and wheat from 8 August 2005 to 10 October 2014, using a Markov chain Monte Carlo method to estimate the SVs and extract the common volatility factor. We find that the volatilities of oil and grain markets are persistent. According to the estimated common volatility factor, high volatility periods match the 2007–2009 recession and the 2007–2008 financial crisis quite well. Finally, the extracted common volatility factor exhibits a distinct pattern.

KEYWORDS:

• Oil and commodity prices
• stochastic volatility
• common volatility factor

JEL CLASSIFICATION:

• C11
• C13
• G10
• Q40

Acknowledgements

This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2014S1A3A2044459).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ We further discuss the volatility function in Section III.

² In this article, we report the results of the extracted latent factors for oil, corn and wheat prices to check for a common trend among the volatility factors and thus do not focus on the results of the univariate stochastic volatility model.

³ Park (2002) shows that the model with the asymptotically homogeneous functions of an integrated process has several useful statistical properties. First, the sample autocorrelations of the squared processes have the same random limitations for all lags, that is, strong persistence. Second, the sample kurtosis is truncated to the left of the innovations kurtosis, that is, leptokurtosis. Since the logistic function belongs to the class of asymptotically homogeneous functions, the model can capture the volatility clustering and fat-tail features of financial and economic time series. Kim, Lee, and Park (2008) point out several desirable properties of the logistic function for the volatility model.

⁴ The symbol N(a,b) denotes a normal distribution with mean a and variance b. G, IG and B represent the gamma distribution, inverse gamma distribution and beta distribution, respectively.

Additional information

Funding

This work was supported by the National Research Foundation of Korea [NRF-2014S1A3A2044459].