step 3.step 3 Analysis of rule out-of expectation problems to possess premature fees

Notice that if your individual risk (q) finds out the bonus in the offer becomes 0. Following just the influenced debtors have a tendency to repay early, whether your ex post interest stays higher. In possible off a lowering interest rate every debtors often pay-off very early. Those people to own just who the benefit in the package remains b usually pay-off early or take up yet another borrowing at a lower interest. The remainder, to own exactly who the personal chance possess know may also pay early. In their eyes the new obtain on contract could be 0.

They reinvests the fresh paid down mortgage at the same interest rate due to the fact the fresh 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. We can therefore exclude this case from further consideration. Read the rest of this entry »