Mean‐variance hedging with basis risk

Xiaole Xue, Jingong Zhang and Chengguo Weng

Applied Stochastic Models in Business and Industry, 2019, vol. 35, issue 3, 704-716

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.

Date: 2019
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https://doi.org/10.1002/asmb.2380

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Persistent link: https://EconPapers.repec.org/RePEc:wly:apsmbi:v:35:y:2019:i:3:p:704-716

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