Optimal futures hedging for energy commodities: An application of the GAS model

• Date: 01 July 2020
• Author: Yingying Xu,Donald Lien
• DOI: http://doi.org/10.1002/fut.22118
• Published date: 01 July 2020

J Futures Markets. 2020;40:1090–1108.wileyonlinelibrary.com/journal/fut1090

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© 2020 Wiley Periodicals, Inc.

Received: 9 November 2019

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Accepted: 25 March 2020

DOI: 10.1002/fut.22118

RESEARCH ARTICLE

Optimal futures hedging for energy commodities: An

application of the GAS model

Yingying Xu

1

|Donald Lien

2

1

School of Economics and Management,

University of Science and Technology

Beijing, Beijing, China

2

College of Business, University of Texas at

San Antonio, San Antonio, Texas

Correspondence

Donald Lien, College of Business,

University of Texas at San Antonio, One

University Circle, San Antonio, TX 78249.

Email: Don.Lien@utsa.edu

Funding information

National Natural Science Foundation of

China, Grant/Award Number: 71873014;

Fundamental Research Funds for the

Central Universities,

Grant/Award Number: 06500106

Abstract

This paper applies generalized autoregressive score‐driven (GAS) models to

futures hedging of crude oil and natural gas. For both commodities, the GAS

framework captures the marginal distributions of spot and futures returns and

corresponding dynamic copula correlations. We compare within‐sample and

out‐of‐sample hedging effectiveness of GAS models against constant ordinary

least square (OLS) strategy and time‐varying copula‐based GARCH models in

terms of volatility reduction and Value at Risk reduction. We show that the

constant OLS hedge ratio is not inherently inferior to the time‐varying alter-

natives. Nonetheless, GAS models tend to exhibit better hedging effectiveness

than other strategies, particularly for natural gas.

KEYWORDS

copula, energy asset, futures, GAS, hedging, score‐driving

JEL CLASSIFICATION

G11; G13; G15; Q43

1|INTRODUCTION

Hedging energy price risk is an important issue considering its effects on the economy (Shrestha, Subramaniam, &

Rassiah, 2017). The futures contract is one of the most favored hedging instruments because of low transaction cost,

high liquidity, extremely low counter‐party risk, low margin requirements, and the ease to take short positions

(Shrestha, Subramaniam, Peranginangin, & Philip, 2018). A constant hedge ratio is determined from the time‐invariant

variances and covariance of spot and futures returns. The time invariance assumption is frequently rejected with real‐

world data and, thus, the ordinary least square (OLS) hedging strategy is deemed inappropriate (Brooks, Henry, &

Persand, 2002; Lien & Yang, 2006). A time‐varying hedging strategy is expected to be more effective and should offer

greater benefits to hedgers.

To capture time‐varying volatilities and correlations among assets, the first class of models considered in the

literature is comprised of observation‐driven models, including the multivariate generalized autoregressive conditional

heteroscedasticity (MGARCH) model of Bollerslev (1986), the dynamic conditional correlation (DCC) model of Engle

(2002), and their variations. The second class is comprised of parameter‐driven models, which include the multivariate

stochastic volatility (SV) models of Chib, Nardari, and Shephard (2006) and Gouriéroux, Jasiak, and Sufana (2009).

Asai, McAleer, and Yu (2006) provide a detailed discussion of the SV model and its relation to GARCH models. Prior

research demonstrates that the DCC‐GARCH model outperforms several alternatives in forecasting volatility and

dynamic correlations (Ding & Vo, 2012; Jain & Biswal, 2016; Sari, Hammoudeh, & Soytas, 2010; Maghyereh, Awartani, &

Tziogkidis, 2017; Mensi, Hammoudeh, Nguyen, & Yoon, 2014; Singhal & Ghosh, 2016).

Creal, Koopman, and Lucas (2013) propose a novel generalized autoregressive score‐driving (GAS) model encompassing

many well‐known time series volatility models such as the GARCH family. Avdulaj and Barunik (2015) apply GAS models

and copula functions to forecast the conditional time‐varying joint distribution of the oil‐stock pairs, yielding statistically

better results for time‐varying dependences and quantiles. Chen and Xu (2019) use a multivariate GAS model to analyze and

forecast volatilities and correlations between crude oil, natural gas, and gold prices. Compared with the classical DCC‐

GARCH model, the GAS approach better captures the volatility persistence and nonlinear interaction effects between crude

oil and gold markets. The GAS model applies the full‐likelihood information instead of first‐and/or second‐order moments

of the observations, which automatically reduces the one‐step‐ahead prediction error of time‐varying parameters. Conse-

quently, the adoption of the GAS framework in capturing time‐varying variances and covariances may affect the hedge ratio

estimation and particularly the effectiveness of optimal futures hedging.

To the best of our knowledge, no study has applied the GAS model to determine the optimal hedge ratio. While the

GAS model encompasses the GARCH family, it is not necessarily superior in its ability to forecast volatility or the

correlation between spot and futures prices, and thus produce greater hedging effectiveness. We will offer an answer

through the empirical studies in this paper. The aim of this paper is twofold. First, we forecast time‐varying conditional

volatilities and conditional correlations between energy spot and futures returns. Second, we compare the hedging

effectiveness of the GAS strategy with other models, such as the GARCH and constant hedge ratios, in terms of

reducing volatility and Value at Risk (VaR). Also, improvements on dollar values for hedging strategies are calculated

and compared. We examine two energy commodity markets, Cushing OK WTI crude oil and Henry Hub natural gas.

We contribute to the literature in several ways. First, we use a GAS (1,1) model to capture the marginal distributions of

energy assets. Second, we offer a copula‐based GAS model to capture the possible conditional dependence between spot and

futures returns of the two energy assets using within‐sample and out‐of‐sample methods. The time‐varying correlation in the

copula model updates following the GAS mechanism. Next, we find that the traditional time‐invariant hedging method is

not necessarily inferior to its time‐varying counterparts, particularly when the goal of hedging is to reduce volatility. When

thegoalistoreduceVaR,time‐varying hedge ratios (in particular, GAS ratios) are superior. Considering transaction costs,

the GAS framework performs particularly well in improving dollar values of hedged positions. Finally, for the above three

criteria, we find the GAS model generally outperforms other dynamic models.

The remainder of this paper is organized as follows. Section 2 briefly reviews the hedge ratio estimation methods.

Section 3 presents the data. Section 4 discusses the empirical findings. Section 5 concludes.

2|COMPETING HEDGE RATIOS

This section provides several methods for estimating the minimum‐variance hedge ratio (MVHR), that is the number of

futures contracts the hedger should buy or sell for each unit of the spot asset to minimize the variance of the hedged

portfolio. Denote

r

ts

and

r

tf

the time series of spot and futures returns, respectively, defined as the difference between

the logarithm of the price at time t+ 1 and time t. Specifically, for daily prices,

r

ts

and

r

tf

represent daily spot and futures

returns, respectively. Consider a hedger who longs an underlying spot asset and opts to short

δt

futures contracts to

minimize the variance of the hedged portfolio. The return on the hedged portfolio,

r

t

P

, is as follows:

rrδr=−

,

tPtsttf(1)

where

()

()

()

()

()

δ

cov r r

var r

ρrr varr

var r

=

,|

|

=

,| |

|

.

t

tstft

tft

tstfttst

tft

1/2

1/2









(2)

The MVHR

δt

is the ratio of the conditional covariance between spot and futures returns to the conditional variance

of the futures return, conditioning on the available information set

t



(Baillie & Myers, 1991). We can further

decompose the conditional covariance into the conditional standard deviations of spot and futures assets and their

correlation, that is

ρ

rr(, | )

.

tstft

Different methods exist for estimating

δ

.

t

We briefly review the most common methods

(Chen, Lee, & Shrestha, 2004; Lien, Tse, & Tsui, 2002) and propose a new method based on the GAS model (Creal

et al. 2013).

XU AND LIEN

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