Methanol futures hedging with skewed normal distribution by copula method

Abstract

As an environmental protection fuel, methanol is widely used in national economy. The tremendous price fluctuation of methanol makes risk avoidance an important issue. However, traditional normal hypothesis in the existing literature underestimates the potential risk and leads to an inefficient hedging strategy, so we studied hedging strategy with methanol futures contracts based on the skewed normal hypothesis. Considering that copula methods allow us to construct a flexible multivariate distribution when solving the problem of asymmetry and nonlinearity, the dependence structure between spot and futures return is modelled through copula functions in this paper. Since likelihood equations do not have explicit solutions in the context of skewed normal, Genetic Algorithm is used to estimate the parameters of a skew normal distribution. To deal with the complexity of the proposed model, the artificial bee colony algorithm is adopted to search for the optimal solutions. Empirical results show that skewed normal distribution can represent the distribution characteristics of return better and improve the hedging effectiveness. Gaussian copula describes the dependence structure of spot and futures quite well. The algorithms designed to obtain the parameters in the marginal distributions and to find the optimal hedge ratio are effective and feasible.

Keywords:

• Futures hedging
• skewed normal distribution
• methanol price
• copula method
• genetic algorithm
• artificial bee colony algorithm

2010 Mathematics Subject Classifications:

• Probability theory and stochastic process
• Computer science

Acknowledgments

This paper is supported by Funds for International Cooperation and Exchange of the National Natural Science Foundation of China (71720107002); National Natural Science Foundation of China (No.71501076); Natural Science Fund of Guangdong (No.2014A030310454); Financial Service Innovation and Risk Management Research Base of Guangzhou; The Raising initial capital for High-level Talents of Central China Normal University (30101190001); Fundamental Research Funds for the Central Universities (CCNU19TD006, CCNU20TD007, CCNU19TS062); Humanities and Social Science Planning Fund from Ministry of Education (Grant No.16YJAZH078).

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Owen [33] defined the function $T(h,a)$ for $h\ge 0$ by $T(h,a)=P(X>h,0<Y<aX)$, for $a\ge 0$, and $T(h,-a)=-T(h,a)$ for negative values of the second argument. Here X and Y are independent and identically distributed standard normal variables. This can be written as a single integral $T(h,a)=\frac{1}{2\pi }{\int }_0^a(1+x^2{)}^{-1}\exp \{-\frac{1}{2}{h}^2(1+x^2)\}\mathrm{d}x$, this also holds when $a\le 0$