Determination of loan interest rate considering bankruptcy and mortgage collection costs

Particularly in Japan, risk management relating to bankruptcy of financed enterprises has become very important to a bank after the collapse of a bubble economy. To obtain suitable revenues, a bank has to apply high interest rates to the enterprises with high risk. When enterprises which have made a secure loan from a bank go bankrupt, a bank forecloses such enterprises from its mortgage to recover the loss incurred. However, in actual circumstances, it may need much cost and effort to do so in Japan. This paper proposes a stochastic model to determine an adequate interest rate, taking account of the probabilities of bankruptcy and mortgage collection, and their costs. Numerical examples are given to illustrate this model and a loan interest rate is determined.