step three.step 3 Studies of the rule out-of expectation injuries to own premature payment
Observe that in case your personal chance (q) knows the main benefit in the bargain will get 0. Following just the affected debtors commonly pay off early, in case loan places Pueblo your ex post interest rate stays higher. But in your situation out-of a bringing down interest rate all debtors will repay very early. Those individuals to own who the main benefit about deal remains b often pay off early or take upwards another type of borrowing in the a reduced rate of interest. The remainder, to possess which the personal exposure has actually knew also pay back very early. To them the new get from the bargain could be 0.
It reinvests brand new reduced mortgage in one rate of interest because the new financing rate
In the model a risk premium exists only for the first credit and not for the second credit. If the debtor takes up the second credit at the low interest rate ( \(_<2l>)\) the interest rate cannot-by assumption-decline any more in future. The bank cannot impose a risk premium on the second credit, because the bank has no damage if the second credit is also prematurely repaid. In the real world it would however recover its handling costs, which are in the model assumed to be 0. This assumption avoids an infinite regress for the calculation of the risk premium without affecting the main point of the analysis. Otherwise, the calculation for the risk premium of the second contract would require the possibility of a third contract and so forth.
Now assume that the first credit is taken up not in the high interest period but in a low interest period \(_<1>=_<1,l>\) . In that case the future, post contractual interest rate can by assumption not further decline. It is either unchanged or higher. Therefore, in this case the only risk of the bank is that the personal risk q realizes. But a damage cannot occur, because an early repayment allows the bank to either invest the money at the same rate or at an even higher rate.