Top

Empirical Economics

Published in:

15-02-2020

Optimal quantile hedging under Markov regime switching

Authors: Donald Lien, Ziling Wang, Xiaojian Yu

Published in: Empirical Economics | Issue 5/2021

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

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.

previous article Does the green inspiration effect matter for stock returns? Evidence from the Chinese stock market

next article Credit default swap spreads: market conditions, firm performance, and the impact of the 2007–2009 financial crisis

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

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.

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.

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.

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.

Alexander C, Prokopczuk M, Sumawong A (2013) The (de)merits of minimum-variance hedging: application to the crack spread. Energy Econ 36:698–707CrossRef

Allen DE, Chang C, Mcaleer M, Singh AK (2018) A cointegration analysis of agricultural, energy and bio-fuel spot, and futures prices. Appl Econ 50(7):804–823CrossRef

Balcilar M, Gungor H, Hammoudeh S (2015a) The time-varying causality between spot and futures crude oil prices: a regime switching approach. Int Rev Econ Finance 40:51–71CrossRef

Balcilar M, Hammoudeh S, Asaba NF (2015b) A regime-dependent assessment of the information transmission dynamics between oil prices, precious metal prices and exchange rates. Int Rev Econ Finance 40:72–89CrossRef

Barbi M, Romagnoli S (2016) Optimal hedge ratio under a subjective re-weighting of the original measure. Appl Econ 48(14):1271–1280CrossRef

Bouoiyour J, Selmi R, Wohar ME (2018) Measuring the response of gold prices to uncertainty: an analysis beyond the mean. Econ Model 75:105–116CrossRef

Brigida M (2014) The switching relationship between natural gas and crude oil prices. Energy Econ 43:48–55CrossRef

Engle RF, Granger CWJ (1987) Co-integration and error correction: representation, estimation and testing. Econometrica 55(2):251–276CrossRef

Ewald CO, Nawar R, Siu TK (2013) Minimal variance hedging of natural gas derivatives in exponential Lévy models: theory and empirical performance. Energy Econ 36(3):97–107CrossRef

Föllmer H, Leukert P (1999) Quantile hedging. Finance Stoch 3(3):251–273CrossRef

Gao Q, He T, Zhang C (2011) Quantile hedging for equity-linked life insurance contracts in a stochastic interest rate economy. Econ Model 28(1–2):147–156CrossRef

Goldfeld S, Quandt RE (1973) A Markov model for switching regressions. J Econom 1(1):3–15CrossRef

Hache E, Lantz F (2013) Speculative trading and oil price dynamic: a study of the WTI market. Energy Econ 36(3):334–340CrossRef

Hamilton JD (1989) A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57(2):357–384CrossRef

Hamilton JD, Susmel R (1994) Autoregressive conditional heteroscedasticity and changes in regime. J Econom 64:307–333CrossRef

Johnson LL (1960) The theory of hedging and speculation in commodity futures. Rev Econ Stud 27(3):139–151CrossRef

Kenourgios D, Samitas A, Drosos P (2008) Hedge ratio estimation and hedging effectiveness: the case of the S&P 500 stock index futures contract. Int J Risk Assess Manag 9(1):121–134CrossRef

Koenker R, Bassett G (1978) Regression quantiles. Econometrica 46(1):33–50CrossRef

Li MYL (2007) Volatility states and international diversification of international stock markets. Appl Econ 39(14):1867–1876CrossRef

Li MYL (2009) The dynamics of the relationship between spot and futures markets under high and low variance regimes. Appl Stoch Models Bus Ind 25(6):696–718CrossRef

Lien D, Shrestha K (2008) Hedging effectiveness comparisons: a note. Int Rev Econ Finance 17(3):391–396CrossRef

Lien D, Tse YK, Tsui A (2002) Evaluating the hedging performance of the constant-correlation GARCH model. Appl Financ Econ 12(11):791–798CrossRef

Lien D, Shrestha K, Wu J (2016) Quantile estimation of optimal hedge ratio. J Futures Mark 36(2):194–214CrossRef

Liu X, Luger R (2018) Markov-switching quantile autoregression: a Gibbs sampling approach. Stud Nonlinear Dyn Econom 22(2):1–33

Muhammad N, Kumar TA, Sana M, Muhammad S (2019) Modeling volatility of precious metals markets by using regime-switching GARCH models. Resour Policy 64:101497CrossRef

Perlin M (2015) MS Regress—the MATLAB package for Markov regime switching models. https://doi.org/10.2139/ssrn.1714016

Qureshi S, Rahman IU, Qureshi F (2018) Does gold act as a safe haven against exchange rate fluctuations? The case of Pakistan Rupee. J Policy Model 40(4):685–708CrossRef

Rakpho P, Yamaka W, Sriboonchitta S (2018) Which quantile is the most informative? Markov switching quantile model with unknown quantile level. IOP Conf Ser J Phys Conf Ser 1053:012121CrossRef

Ramchand L, Susmel R (1998) Volatility and cross correlation across major stock markets. J Empir Finance 5:397–416CrossRef

Selmi R, Mensi W, Hammoudeh S, Bouoiyour J (2018) Is Bitcoin a hedge, a safe haven or a diversifier for oil price movements? A comparison with gold. Energy Econ 74(8):787–801CrossRef

Shrestha K, Subramaniam R, Peranginangin YA, Philip SSS (2018) Quantile hedge ratio for energy markets. Energy Econ 71(3):253–272CrossRef

Terry E (2005) Minimum-variance futures hedging under alternative return specifications. J Futures Mark 25(6):537–552CrossRef

Torró H (2011) Assessing the influence of spot price predictability on electricity futures hedging. J Risk 13(4):31–61CrossRef

Tsai JT, Wang JL, Tzeng LY (2020) On the optimal product mix in life insurance companies using conditional value at risk. Insur Math Econ 46(1):235–241CrossRef

Wang Y, Yin G (2012) Quantile hedging for guaranteed minimum death benefits with regime switching. Stoch Anal Appl 30(5):799–826CrossRef

Wang Y, Hu C, Yan L (2015) Hedging with futures: does anything beat the naïve hedging strategy? Manag Sci 61(12):2870–2889CrossRef

Wang Y, Geng Q, Meng F (2019) Futures hedging in crude oil markets: a comparison between minimum-variance and minimum-risk frameworks. Energy 181:815–826CrossRef

Yamaka W, Rakpho P, Sriboonchitta S (2018) Bayesian Markov switching quantile regression with unknown quantile \(\tau \): application to stock exchange of Thailand (SET). Thai J Math, Special Issue: Structural change modeling and optimization in econometrics 2018, 1–13

Ye W, Zhu Y, Wu Y, Miao B (2016) Markov regime-switching quantile regression models and financial contagion detection. Insur Math Econ 67:21–26CrossRef

Title: Optimal quantile hedging under Markov regime switching
Authors: Donald Lien
Ziling Wang
Xiaojian Yu
Publication date: 15-02-2020
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 5/2021
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-020-01831-5

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft"

Springer Professional "Wirtschaft+Technik"

Other articles of this Issue 5/2021

Why do Turkish REITs trade at discount to net asset value?

Credit default swap spreads: market conditions, firm performance, and the impact of the 2007–2009 financial crisis

Forecasting exports across Europe: What are the superior survey indicators?

Does the green inspiration effect matter for stock returns? Evidence from the Chinese stock market

A simple wavelet-based test for serial correlation in panel data models

The effect of training on workers’ perceived job match quality