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Abstract
This study investigated the cross-markets price changes, volatility, and shock transmission mechanism among gasoline, crude oil, and diesel spot markets. An asymmetric time-varying volatility model is used to reveal the hidden dynamic shock transmission mechanism among the markets. An iterative optimization Newton–Raphson algorithm is used in the nonlinear estimation procedures by updating the outer product of the gradient vector. The estimated results are used in quantifying the cross-market risk, optimal portfolio holding, and hedging among the energy markets.
Acknowledgment
The author would like to gratefully acknowledge the anonymous referees for their helpful comments on an earlier version of the article. This research was supported by MOHE and Multimedia University (SPSCR).
Notes
Besides this interdependence connection, the dynamic relationship between energy market and other economic indicators can also be studied under the cointegration theory with long-term or equilibrium relationships. For two non stationary time series, the cointegration analysis in econometric focused on the Engle and Granger (Citation1987) and Johansen and Juselius (Citation1990) approaches whereas the Econophysics often implemented the wavelet methods or detrended fluctuation analysis (Podobnik and Stanley, Citation2008; Razdan, Citation2004; Zhou, Citation2008) in determining the time series cross-correlations.
Other econophysics methodologies commonly used to examine the international financial market comovements can be found in Lee (Citation2004), Barndorff-Nielsen and Shephard (Citation2004), and Rua and Nunes (Citation2009). The comprehensive literatures of parametric and nonparametric volatility measurements are documented in Andersen et al. (Citation2010), Malliavin and Mancino (Citation2002), and Zhou (Citation1996).
A crude stream produced in Texas and Southern Oklahoma which served as a reference or “marker” for pricing a number of other crude streams and which is traded in the domestic spot market at Cushing, Oklahoma (Unit: USD per barrel).
The location specified in either spot or futures contracts for delivery of a product in New York Harbor.
An ARCH model frequently represented by a regression model in the form of r t = x t ’β +a t . Where x t ’ is a column vector.
For example the full parameterization vector half VECH method required 21 instead of 11 parameters in the unrestricted BEKK for the simplest 2 × 2 multivariate specification. It is also worth noting that under the rank one matrices condition for the coefficient matrices, the VECH and BEKK are both positive semidefinite.
The covariance equation only reacted to the asymmetric effect if either both the markets encountered leverage effect.
For univariate model, replaced the H
t
and a’
t
H
t
a
t
with and
, respectively.
For long position investor, they invest as buying a stock, holding it while it appreciates, and eventually sell it for profit. They encounter risk when the price of the stock decreases. On the other hand, the short trading position investors react exact opposite where they firstly sell the stock with the intention to later buy it back at a lower price. Therefore, the risk comes from a rise in the price of the stock. Long financial position refers to the left-tail distribution while the short position concerns about the right-tail behavior.
This referred to diversified VaR where the correlation (either positive or negative but not equivalent to unity) exists between two markets. The diversified VaR is commonly used to determine the resources limitation therefore the portfolio can minimize the risk and at the same time maximize the profit.
Notes: *indicated 5% significance level.
*Indicated 5% significance level.
Notes: Variance-covariance equations based on Eq. (8); ** indicated 5% significance levels
Notes: Standardized residual, .
For h-day horizon, one may use the square root of time rule under the Risk Metrics (1995) with .