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Mean‐variance hedging with basis risk

Author

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  • Xiaole Xue
  • Jingong Zhang
  • Chengguo Weng

Abstract

Basis risk arises in a number of financial and insurance risk management problems when the hedging assets do not perfectly match the underlying asset in a hedging program. Notable examples in insurance include the hedging for longevity risks, weather index–based insurance products, variable annuities, etc. In the presence of basis risk, a perfect hedging is impossible, and in this paper, we adopt a mean‐variance criterion to strike a balance between the expected hedging error and its variability. Under a time‐dependent diffusion model setup, explicit optimal solutions are derived for the hedging target being either a European option or a forward contract. The solutions are obtained by a delicate application of the linear quadratic control theory, the method of backward stochastic differential equation, and Malliavin calculus. A numerical example is presented to illustrate our theoretical results and their interesting implications.

Suggested Citation

  • Xiaole Xue & Jingong Zhang & Chengguo Weng, 2019. "Mean‐variance hedging with basis risk," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 35(3), pages 704-716, May.
    • Handle: RePEc:wly:apsmbi:v:35:y:2019:i:3:p:704-716
    DOI: 10.1002/asmb.2380
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    References listed on IDEAS

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    1. Patrick L. Brockett & Mulong Wang & Chuanhou Yang, 2005. "Weather Derivatives and Weather Risk Management," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 8(1), pages 127-140, March.
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