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Erschienen in: Empirical Economics 5/2021

15.02.2020

Optimal quantile hedging under Markov regime switching

verfasst von: Donald Lien, Ziling Wang, Xiaojian Yu

Erschienen in: Empirical Economics | Ausgabe 5/2021

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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.

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Fußnoten
1
Föllmer and Leukert (1999) introduce quantile hedging where the strategy is chosen to maximize the probability of a successful hedge for a given budget constraint. It can be restructured as a dynamic version of minimizing VaR (value at risk). In other words, the Föllmer–Leukert (FL) quantile hedging attempts to minimize the quantile risk of the hedged portfolio, which is quite different from Lien et al. (2016). The FL quantile hedging has been applied to reduce systematic mortality risk for life insurance companies (e.g., Wang and Yin 2012; Tsai et al. 2020; Gao et al. 2011). Qureshi et al. (2018), Selmi et al. (2018) and Bouoiyour et al. (2018) find that, via FL quantile hedging, gold could help to protect against the exposure to uncertain risks.
 
2
Rakpho et al. (2018) and Yamaka et al. (2018) independently propose the Markov regime switching quantile model with unknown quantile level. Rakpho et al. (2018) estimate the parameters via the maximum likelihood estimation (MLE) method and Yamaka et al. (2018) adopt the Bayesian approach.
 
3
Alternatively, the MRS models can be estimated with Bayesian inference via Gibbs sampling. Liu and Luger (2018) consider a Markov-switching quantile autoregression model and apply the Gibbs sampling approach to analyze and forecast the US real interest rate. While Liu and Luger (2018) focuses on the univariate quantile framework, we consider bivariate quantile regression models.
 
4
Because a given spot return corresponds to different quantiles whether it is ranked under state 1 distribution, state 2 distribution, or one-state distribution, there is not a deterministic relationship between the three quantile hedge ratios calculated at any spot return. Thus, the U shape for hedge ratio in state 2, coupled with a flat curve in state 1, is not in conflict with the inverted U shape for the one-state case.
 
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Metadaten
Titel
Optimal quantile hedging under Markov regime switching
verfasst von
Donald Lien
Ziling Wang
Xiaojian Yu
Publikationsdatum
15.02.2020
Verlag
Springer Berlin Heidelberg
Erschienen in
Empirical Economics / Ausgabe 5/2021
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI
https://doi.org/10.1007/s00181-020-01831-5

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