This paper proposes a new intelligent design method for the collar option of weather derivatives. They play an important role to hedge risks caused by meteorological conditions. The collar option implies the transaction between two companies that take a complementary stance to risks. Such an idea is applicable to power and gas companies. This paper focuses on the equivalence of the payoffs in the collar option that sets up to equalize the stochastic characteristics of payoffs. The objective function may be expressed as the minimization of a sum of the stochastic moments from the first to the fourth. To realize it, it is necessary to optimize the parameters the payoff function that describes the nonlinear relationship between a weather index and the payoffs. In this paper, MVMO-SH of evolutionary computation is proposed for optimizing them. It is one of high-performance evolutionary computation with the nonlinear mapping function. Also, the Bootstrap method is introduced to evaluate the stochastic moments due to the effectiveness for data analysis with insufficient samples. The proposed method is successfully applied to real data of the weather derivative.