Pricing method and applications for the farmer's joint liability based on intensity model and Monte Carlo simulation

Abstract

This paper studies the pricing problem of group lending using the strength model and the Monte Carlo simulation method. Simulating the default process of farmers with a Poisson process, this paper describes the default distribution for farmers, and based on which the paper establishes the pricing model of the group lending and obtains the critical number of the defaulted farmers and the default probability for the group. Next, this paper introduces the t-Copula function to describe the default correlation between farmers, and obtains the partially analytical solution of the loan rate for the group lending, and it also provides the Monte Carlo simulation algorithm for the pricing of group lending based on t-Copula function. Finally, this paper carries out the Monte Carlo simulation algorithm on the pricing problem of group lending with three and five peasant households through an example, and discusses the relationship between the loan rate and each of the influencing factors in the pricing model of the group lending.