Rationales of mortgage insurance premium structures

Journal of Real Estate Research, The, 1997 by Barry Dennis, Chionglong Kuo, Tyler T Yang

While both the Upfront case and the Financing case have identical degrees of termination year subsidization, the total premium cost to the Financing case prepayers is greater than that to the Upfront case prepayers because the Financing case has a greater amount of extra defaulter subsidization than the Upfront case. In the Upfront case both prepayers and defaulters pay the same upfront premium, none of which is refunded no matter what the timing or reason for termination. In contrast, under the Financing case, the premium is included in the loan principal amount and amortized over the life of the loan. Early prepayers must pay the unpaid principal balance and the unpaid premium.

However, when a borrower defaults he defaults both on the unpaid principal balance and on the unpaid premium. Thus, the present value of the amortized premium equals the amount of the upfront premium (as long as the discount rate equals the mortgage interest rate) for prepayers, but is less than the amount of the upfront premium for defaulters.

Therefore, non-defaulters must pay a higher premium to make up for the nonpayment by defaulters, resulting in extra defaulter subsidization.

After year 11, total premiums in the Refund case become increasingly lower than those in the Annual case. This occurs because the Refund case has significantly less extra defaulter subsidization than the Annual case does after year 11. While both the Annual case and the Refund case match expected future losses fairly closely through year 11, at that point in time defaults decline markedly. This decline in future defaults is reflected in the refund schedule of the Refund case, but is not reflected in the Annual case which continues to remain unchanged. Under the Annual case, defaulters avoid paying annual premiums for the remainder of the loan period. However, since defaulters lose their refund under the Refund case, they effectively still pay the premium that covers the remainder of the loan term. Thus, the Refund case has a reduced extra defaulter subsidization.

Exhibit 3 displays similar information for defaulters. The Financing case is the most preferred for all but the latest defaulters. This general preference for the Financing case is due to the heavy implicit extra defaulter subsidization. The Upfront case and the Refund case have substantial implicit termination year subsidization for defaulters, while the Annual case and the Financing case have less. Thus, for both prepayers and defaulters, upfront premiums have substantial termination year subsidization. While for prepayers, the Financing case has substantial termination year subsidization, for defaulters this case has much less termination year subsidization. This occurs because, since defaulters default on the unpaid amortized premium, the later they default the more total premium they pay. Non-defaulters pay the same total present value premium regardless of when they prepay. In contrast, the Refund case has substantial termination year subsidization for defaulters since they give up their refund upon default and therefore pay the same total premium regardless of when they default. The Refund case has the least termination year subsidization for prepayers.