Optimal quantile hedging under Markov regime switching
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Optimal quantile hedging under Markov regime switching Donald Lien1 · Ziling Wang2 · Xiaojian Yu2,3 Received: 28 October 2019 / Accepted: 4 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this study, we introduce a new quantile hedging method by extending the conventional quantile hedging with two-state Markov regime switching models. Using daily data from 16 futures markets, we discover that the conventional quantile hedge ratio displays an inverted U shape to various extents for different futures. When looking into high- and low-volatility states, quantile hedge ratios show different results compared with conventional models. While the quantile hedge ratio in low-volatility state is relatively flat, in high-volatility state, the quantile hedge varies with the spot return distribution and displays a U-type relationship. Moreover, the U shape is more prominent for agricultural futures and less prominent for others. Also, by comparing hedging effectiveness, the quantile hedge strategy is found to be more effective than the no-hedge strategy and the hedging strategy derived from error correction models. Keywords Futures · Quantile hedging · Markov regime switching · Hedge ratio JEL Classification C14 · C22 · G13
1 Introduction An essential function of futures is to hedge the risk of spot prices. The hedge ratio is the proportion of the position in a futures contract to the position of the spot asset. Since Johnson (1960) proposes the minimum-variance (MV) hedge ratio by minimizing the variance of the hedged portfolio, the MV method has been widely adopted in practice and academic (e.g., Terry 2005; Lien and Shrestha 2008; Torró 2011; Alexan-
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Xiaojian Yu [email protected]
1
College of Business, The University of Texas at San Antonio, San Antonio, TX, USA
2
School of Economics and Commerce, South China University of Technology, Guangzhou, Guangdong, China
3
Research Center of Financial Engineering, South China University of Technology, Guangzhou, Guangdong, China
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D. Lien et al.
der et al. 2013; Ewald et al. 2013; Wang et al. 2015; Barbi and Romagnoli 2016; Wang et al. 2019). Many statistical methods are applied to estimate the optimal hedge ratio, including ordinary least squares (OLS), error correction model (ECM), conditional heteroskedastic (ARCH or GARCH) model, and random coefficient model. The main differences in these methods are the conditional information set and the static versus dynamic nature of the hedge ratio. Lien et al. (2002) find that the OLS hedge ratio performs better than the VGARCH hedge ratio because the forecasts generated by the GARCH models fluctuates significantly. Following the study of Lien et al. (2016), we estimate the quantile hedge ratio with the ECM which performs better than the OLS according to Kenourgios et al. (2008). The optimal hedge ratio estimated by the conventional regression method is based on the expected correlation between spot and futures returns, which neglects the relationships between the two returns at differe
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