Pricing Method And Applications For The Farmer’s Joint Liability Based On Intensity Model And Monte Carlo Simulation

This paper mainly studies the pricing problem of group lending, which is of great importance to the business development of microfinance institutions. Working out the loan rate can effectively guide the actual business operation, and the loan rate for microfinance institutions can neither be too high nor too low. A too high interest rate will undoubtedly increase the lender’s burden and violate lender’s benefits. But if interest rate is limited and it is low, then new microfinance institutions are difficult to emerge, and the existing microfinance institutions are also difficult to maintain their business, thus the development of rural finance cannot be promoted. Above all, during the process when the marketization of interest rate in our country is gradually deepened, and under the background when the rate control for microfinance institutions is gradually loosed, the theoretical research on rate of group lending is of high importance.The paper studies the pricing problem of group lending using the strength model and the Monte Carlo simulation method. It makes an analysis on group selection behavior and group scale when forming a group, and obtains the relationships between loan rate, the recovery rate when default, the rate of return when project succeeds and the critical number of defaulted farmers. Simulating the default process of farmers with a Poisson process, the paper establishes the pricing model of the group lending and obtains the critical number of defaulted farmers and the default probability for the group. As the existing of default correlation in group lending, the default form changes from individual default to group default, and thus influencing the independence of repayment for group members. 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.