Optimal Hedging with Basis Risk under Mean-Variance Criterion

41 Pages Posted: 4 Apr 2017 Last revised: 10 May 2019

See all articles by Jingong Zhang

Jingong Zhang

University of Waterloo - Department of Statistics and Actuarial Science

Ken Seng Tan

University of Waterloo

Chengguo Weng

University of Waterloo

Date Written: February 21, 2017

Abstract

Basis risk occurs naturally in a number of financial and insurance risk management problems. A notable example is in the context of hedging a derivative where the underlying security is either non-tradable or not sufficiently liquid. Other examples include hedging longevity risk using index-based longevity instrument and hedging crop yields using weather derivatives. These applications give rise to basis risk and it is imperative that such a risk needs to be taken into consideration for the adopted hedging strategy. In this paper, we consider the problem of hedging a European option using another correlated and liquidly traded asset and we investigate an optimal construction of hedging portfolio involving such an asset. The mean-variance criterion is adopted to evaluate the hedging performance, and a subgame Nash equilibrium is used to define the optimal solution. The problem is solved by resorting to a dynamic programming procedure and a change-of-measure technique. A closed-form optimal control process is obtained under a diffusion model setup. The solution we obtain is highly tractable and to the best of our knowledge, this is the first time the analytical solution exists for dynamic hedging of general European options with basis risk under the mean-variance criterion. Examples on hedging European call options are presented to foster the feasibility and importance of our optimal hedging strategy in the presence of basis risk.

Keywords: Basis Risk; Optimal Hedging; Time Consistent Planning; Mean-Variance

Suggested Citation

Zhang, Jingong and Tan, Ken Seng and Weng, Chengguo, Optimal Hedging with Basis Risk under Mean-Variance Criterion (February 21, 2017). Insurance: Mathematics and Economics, Vol. 75, 1-15, 2017, Available at SSRN: https://ssrn.com/abstract=2921357 or http://dx.doi.org/10.2139/ssrn.2921357

Jingong Zhang

University of Waterloo - Department of Statistics and Actuarial Science ( email )

200 University Avenue West
Waterloo, Ontario N2L 3G1
Croatia

Ken Seng Tan

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1
Canada

Chengguo Weng (Contact Author)

University of Waterloo ( email )

M3-200 Univ Ave W
Waterloo, Ontario N2L3G1
Canada
(1)888-4567 ext.31132 (Phone)

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