Before revision:   We aim at establishing explicitly the value of such a loan and ranges of fair values of key parameters : this loan size, interest rate,  fee for providing such a service and quantity of this automatic termination clause and relationships among these parameters as well as the optimal terminable stopping times .
After revision:  Mathematically, it is a kind of optimal stopping problems arising from the pricing of financial products which is first revealed. We aim at establishing explicitly the value of such a loan and ranges of fair values of key parameters : this loan size, interest rate, fee for providing such a service and quantity of this automatic termination clause and relationships among these parameters as well as the optimal terminable stopping times .