Index Insurance Design

36 Pages Posted: 12 Sep 2018

See all articles by Jinggong Zhang

Jinggong Zhang

Nanyang Technological University (NTU) - Nanyang Business School

Ken Seng Tan

University of Waterloo

Chengguo Weng

University of Waterloo

Date Written: August 30, 2018


In this article, we study the problem of optimal index insurance design under an expected utility maximization framework. For general utility functions, we formally prove the existence and uniqueness of optimal contract, and develop an effective numerical procedure to calculate the optimal solution. For exponential utility and quadratic utility functions, we obtain analytical expression of the optimal indemnity function. Our results show that the indemnity can be a highly non-linear and even non-monotonic function of the index variable in order to align with the actual loss variable so as to achieve the best reduction in basis risk. Due to the generality of model setup, our proposed method is readily applicable to a variety of insurance applications including index- linked mortality securities, weather index agriculture insurance and index-based catastrophe insurance. Our method is illustrated by a numerical example where weather index insurance is designed for protection against the adverse rice yield using temperature and precipitation as the underlying indices. Numerical results show that our optimal index insurance significantly outperforms linear-type index insurance contracts in terms of reducing basis risk.

Suggested Citation

Zhang, Jinggong and Tan, Ken Seng and Weng, Chengguo, Index Insurance Design (August 30, 2018). Available at SSRN:

Jinggong Zhang

Nanyang Technological University (NTU) - Nanyang Business School ( email )

Singapore, 639798

Ken Seng Tan

University of Waterloo ( email )

Waterloo, Ontario N2L 3G1

Chengguo Weng (Contact Author)

University of Waterloo ( email )

M3-200 Univ Ave W
Waterloo, Ontario N2L3G1
(1)888-4567 ext.31132 (Phone)

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