Effects of skewness and kurtosis on production and hedging decisions: a skewed t distribution approach

Abstract

This paper assumes that the spot price follows a skewed Student t distribution to analyze the effects of skewness and kurtosis on production and hedging decisions for a competitive firm. Under a negative exponential utility function, the firm will not over-hedge (under-hedge) when the spot price is positively (negatively) skewed. The extent of under-hedge (over-hedge) decreases as the forward price increases. Compared with the mean-variance hedger, the producer will hedge more (less) when negative (positive) skewness prevails. In addition, an increase in the skewness reduces the demand for hedging. The effect of the kurtosis, however, depends on the sign of the skewness. When the spot price is positively (negatively) skewed, an increase in kurtosis leads to a smaller (larger) futures position.

Keywords:

• forward contract
• hedging
• skewed normal distribution
• skewed t distribution

JEL Classification:

• G11
• G32

Acknowledgements

The authors wish to acknowledge two anonymous referees and an associate editor for their comments and suggestions.

Notes

1. In this paper, we use forward and futures interchangeably.

2. Assume that there is a single risky asset, the return of which is skewed normally distributed. Eling, Kattumannil, and Tibiletti (2010) prove that positive skewness promotes the demand for the risky asset.

3. Some properties of the modified Bessel function are listed in Appendix 1. For discussion on the Bessel function, see Abramowitz and Stegun (1972).

4. The proofs of these two statements are contained in Appendix 2.

5. The difference is that the former hedger chooses the simple method by intentionally ignoring higher moments, whereas the latter hedger makes an incorrect assumption about the spot price distribution. The outcomes are the same though.

6. A direct comparison is possible if we adopt Azzalini–Capitanio skewed t distributions. As noted in Section 2, this approach does not produce an easy-to-use closed-form expression for the moment-generating function.