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Mean‐variance hedging with basis risk
Author(s) -
Xue Xiaole,
Zhang Jingong,
Weng Chengguo
Publication year - 2018
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.2380
Subject(s) - basis risk , basis (linear algebra) , variance (accounting) , econometrics , stochastic differential equation , mathematics , risk management , economics , actuarial science , malliavin calculus , asset (computer security) , mathematical economics , quadratic equation , time consistency , computer science , differential equation , capital asset pricing model , finance , stochastic partial differential equation , mathematical analysis , geometry , accounting , computer security
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.