Mean‐variance hedging with basis risk

• Main Authors: Xue, Xiaole, Zhang, Jingong, Weng, Chengguo
• Other Authors: Nanyang Business School
• Format: Article
• Language: English
• Published: 2021
• Subjects: Business::Finance; Optimal Hedging; Basis Risk
• Online Access: https://hdl.handle.net/10356/149141
• Institution: Nanyang Technological University

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.