A Multivariate Markov Regime‐Switching High‐Frequency‐Based Volatility Model for Optimal Futures Hedging

• Date: 01 November 2017
• Author: Hsiang‐Tai Lee,Yu‐Sheng Lai,Her‐Jiun Sheu
• Published date: 01 November 2017
• DOI: http://doi.org/10.1002/fut.21842

A Multivariate Markov Regime-Switching

High-Frequency-Based Volatility Model

for Optimal Futures Hedging

Yu-Sheng Lai , Her-Jiun Sheu, and Hsiang-Tai Lee *

This study proposes a multivariate Markov regime-switching high-frequency-based volatility

(MRS-HEAVY) model for modeling the covariance structure of spot and futures returns, and

estimating the associated hedge ratios. S&P 500 equity index data are used in estimations, and

the results reveal that the MRS-HEAVY model has a shorter response time than that of the

Markov regime-switching GARCH model; this difference is more pronounced in the high-

volatility regime than in the low-volatility regime. Out-of-sample hedging exercises illustrate

that the MRS-HEAVY exhibits superior hedging performance in terms of both variance

reductions and utility gains; it is robust even when transaction costs are considered. © 2017

Wiley Periodicals, Inc. Jrl Fut Mark 37:1124–1140, 2017

1. INTRODUCTION

Generalized autoregressive conditional heteroskedasticity (GARCH) models and their

variants are widely applied for volatility modeling. Models within the GARCH framework use

daily (squared) returns to determine volatility levels (Bollerslev, 1986; Engle, 1982).

However, squared returns offer limited information on ex-post return variation (Andersen &

Bollerslev, 1998). Therefore, standard GARCH models might perform poorly in situations

where volatility levels change rapidly (Andersen, Bollerslev, Diebold, & Labys, 2003).

Recent studies have documented that incorporating realized variances

1

into standard

GARCH (known as GARCH-X models) increases explanatory power and improves predictive

Yu-Sheng Lai is Associate Professor at Department of Banking and Finance, National Chi Nan University, 1,

University Rd., Puli, Nantou Hsien, Taiwan. Her-Jiun Sheu is Professor at Department of Finance, Ming

Chuan University, 250, Zhong Shan N. Rd., Sec. 5, Shihlin District, Taipei, Taiwan. Hsiang-Tai Lee is

Professor at Department of Banking and Finance, National Chi Nan University, 1, University Rd., Puli,

Nantou Hsien, Taiwan. We are grateful to professor Bob Webb (editor) and an anonymous referee for the

valuable suggestions to improve the paper. We thank participants at the 30th International French Finance

Association Conference at Lyon, France, and the International Banking, Economics and Finance Association

(IBEFA) Conference at San Francisco, USA, for their helpful comments. We also acknowledge financial

support from the Ministry of Science and Technology of Taiwan under grant number 99-2410-H-260-028.

*Correspondence author, Department of Banking and Finance, National Chi Nan University, 1, University Rd.,

Puli, Nantou Hsien 54561, Taiwan. Tel: þ886-49-2910960 ext. 4648, Fax: þ886-49-2914511, e-mail:

sagerlee@ncnu.edu.tw

Received October 2015; Accepted December 2016

1

Using HF data, a number of realized measures of volatility (e.g., the commonly used realized variance estimator of

Andersen, Bollerslev, Diebold, & Labys, 2001 and Barndorff-Nielsen and Shephard, 2002) have been proposed for

true asset return variation; Andersen, Bollerslev, Christoffersen, and Diebold (2006) and McAleer and Medeiros

(2008) have recently reviewed these methods.

The Journal of Futures Markets, Vol. 37, No. 11, 1124–1140 (2017)

© 2017 Wiley Periodicals, Inc.

Published online 2 March 2017 in Wiley Online Library (wileyonlinelibrary.com).

DOI: 10.1002/fut.21842

ability for the dynamic features of volatility (Engle, 2002; Koopman, Jungbacker, & Hol,

2005). High-frequency-based volatility (HEAVY) models can adjust more quickly to changes

in volatility than standard GARCH models can (Hansen, Huang, & Shek, 2012; Shephard &

Sheppard, 2010).

Precisely forecasting the covariance structure of spot and futures is essential to optimal

futures hedging, because the optimal hedge ratio is computed as the conditional covariance

of spot and futures returns over the conditional variance of futures returns. HEAVY-type

models have produced precise forecasts of the conditional covariance matrix. On this basis,

Lai and Sheu (2010) and Sheu and Lai (2014) calculated the hedge ratio using high-

frequency (HF) data and discovered that the gains on hedging are substantial, compared with

models that include daily prices only. This result illustrates the importance of applying

HEAVY models in futures hedging.

Another strand in the literature focuses on forecasting the covariance structure of spot

and futures returns with regime-switching GARCH models. Lee and Yoder (2007a) and

Alizadeh, Nomikos, and Pouliasis (2008) have applied a regime-switching BEKK GARCH;

Lee and Yoder (2007b) suggested a regime-switching varying correlation GARCH; Lee

(2010) adopted a regime-switching dynamic conditional correlation GARCH; and Sheu and

Lee (2014) proposed a multi-chain Markov regime-switching GARCH for calculating

optimal hedge ratios by forecasting the conditional second moments. A common finding has

been that incorporating regime switching into multivariate GARCH models enhances the

effectiveness of futures hedging.

If the joint distribution of spot and futures returns and hence the hedge ratio is state

dependent, a more flexible regime switching model that can swiftly adapt to market changes

in a highly volatile regime has potential to improve the forecasts of the optimal hedge ratio

and thus the effectiveness of futures hedging. This is the first study to apply a multivariate

high-frequency-based regime-switching model in modeling dynamic spot and futures

covariance structures. This study fills this gap in the literature by proposing a multivariate

Markov regime-switching high-frequency-based volatility (MRS-HEAVY) model for futures

hedging. The contribution of this paper to this field of research is twofold. First, the proposed

MRS-HEAVY model possesses both HF and regime-switching properties. These dual

properties allow us to investigate whether the response time of a HEAVY model is shorter

than that of a GARCH model in the high volatility regime, as well as whether MRS-GARCH

models can efficiently track sudden changes in the covariance structure of spot and futures

markets under market turmoil. Second, the proposed MRS-HEAVY model is applied in S&P

500 spot and futures contracts as well as out-of-sample hedging exercises. The results

demonstrate that the MRS-HEAVY model exhibits superior hedging performance in terms of

both variance reduction and utility gains.

The remainder of the paper is org anized as follows. The specifications of the MRS-

HEAVY model are presented in Secti on 2. As reported in Section 3, a simulati on study is

conducted to examine the per formance of the proposed mode l. The optimal hedge ratio

and measurements of hedging performance are described in Section 4, and Section 5

presents the data descripti on and empirical results. Sectio n 6 provides the conclusions of

the study.

2. MRS-HEAVY MODEL

The multivariate HEAVY models introduced by Noureldin et al. (2012) are in a new class of

models that use HF data to describe the dynamic features of return volatility. Compared with

standard multivariate GARCH models, which utilize low-frequency (LF) data, HEAVY

A MRS-HEAVY Model for Optimal Futures Hedging 1125