See that should your personal exposure (q) knows the benefit on the offer will get 0. Upcoming just the inspired debtors have a tendency to pay back very early, if for example the ex lover post interest rate stays large. In the actual situation out-of a lowering interest rate the debtors have a tendency to pay-off very early. People for exactly who the benefit throughout the price remains b tend to pay very early and take upwards a different sort of borrowing from the bank at the less interest. The rest, having exactly who the personal risk features knew also repay early. To them the get about offer could be 0.
They reinvests brand new repaid mortgage at the same interest once the the brand new lending speed
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. The expected gain of the debtor from the contract is then
In the event the chance premium is roofed explicitly, we become on requested obtain regarding a credit price, that has been finished during a premier interest months
Which constellation in the design, where in fact the premature payment off borrowing from the bank grounds zero problems and you will for that reason zero rate of interest mark up is not then believed from inside the these investigation.
If the legal remedy for early repayment is expectation damages the damage from early repayment is the difference between the contractual and the post-contractual interest rate \(_<1>-_<2>\) . The bank can invest the repaid money at an interest rate of \(_<2>\) . It can, for instance, buy mortgage bonds on the secondary age payment results if and only if \(_<1>>_<2>\) . Otherwise the differential method of damage calculation results in a damage award of zero. The compensation payment is therefore
Let us now assume that after the conclusion of the contract the market interest rate falls, but the benefit from the contract remains at b. We get an outcome which is different in comparison with the result under a right of premature repayment. The debtor wants to end the contract and take out a new mortgage at the low interest rate. With expectation damages as remedy for breach of contract her gain would be \((b-_<2>)-\left( _<1>-_<2>\right)=b-_<1>\) . The term in the first bracket is the consumer’s gain from the new mortgage contract and the term in the second bracket denotes the amount of damages to be paid. The early repayment motivated by the lower interest rate does not result in a gain that is higher than the gain from performance of the contract as originally concluded. Therefore, no early repayment results for taking up a new credit if interest rates decrease after contract formation (Table 2).