Calculation of crop insurance premium based on dependence among yield price, crop yield, and standard rainfall index using vine copula

Abstract

The aim of this research is to discuss the use of Vine Copula with dimension for measuring the dependencies among yield price, crop yield, and standard rainfall index, to calculate the insurance premium. This research is focused at Dlingo, Bantul, where the farmers are depend on rainfall or other water resources. The adoption of standard rainfall index CHS as part of Indemnity decision is reasonable as there are strong correlation between amount of rainfall and yield. In D-Vine structure, the most proper copula to explain the dependence between yield price and the crop yield is Joe copula with θ=1.76 and τ=0.3, while for the crop yield and the standard rainfall index is Frank copula with θ=4.98 and τ=0.46. The simulations data shows that the insurance premium of crop insurance based on rainfall index will give various options of premium rather than traditional crop insurance. The lower value of CHSα will give a lower premium for farmers, however it will impact the decision of indemnity since the indemnity will be paid if CHS t ≤ CHSα. The most important thing for this insurance contract is there are two layers for insurer to claim the policy, one is the CHSt related to CHS α and Ip related to revenue I. In fact, if the value of CHSα is increasing the net single premium will also increase. For similar target income, it can be concluded that the premiums for insurance based on CHS are less expensive compared to traditional crop insurance.