Mean‐variance hedging with basis risk

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 annuitie...

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Bibliographic Details
Published inApplied stochastic models in business and industry Vol. 35; no. 3; pp. 704 - 716
Main Authors Xue, Xiaole, Zhang, Jingong, Weng, Chengguo
Format Journal Article
LanguageEnglish
Published Bognor Regis Wiley Subscription Services, Inc 01.05.2019
Subjects
basis risk
BSDE
Control theory
Differential calculus
Differential equations
Insurance
Malliavin derivative
mean‐variance analysis
optimal hedging
Risk management
stochastic LQ control
Time dependence
Variance
Weather
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Summary: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.
Bibliography:Present Address
ISSN:1524-1904
1526-4025
DOI:10.1002/asmb.2380