逆房貸抵押品的處置時間對保險費率的影響

The Impact of the Disposition Time of Reverse Mortgage Collaterals on Insurance Premiums

「不動產逆向抵押型房貸方案」，讓年長者的自有住宅，轉換為提供生活所需現金流之房產權益，發揮居住和融資的雙重功能。本文考慮當事人的平均餘壽、房價波動、折舊率、及市場利率等隨機因素，推導出當事人（借方）的最大可貸額度與銀行（貸方）每月須支付的金額。契約到期時，當貸款餘額大於當時房價，銀行可向保險公司索賠。本文以保險公司的「預期索賠損失的現值」等於「預期抵押貸款保險費之現值」損益兩平為前提，建議（保險公司）保險費率之設定。並針對（銀行）處置抵押品平均所花費的時間，探討處置時間點與保險費率的關聯性，希望藉由保險機制的引入，增加參與此方案的誘因，擴大其實施效能，並為設計與修訂此方案，提供關鍵資訊。

Reverse mortgage plans (RM) allow the elderly (borrowers) to employ their own real estate as both housing and a financing instrument throughout their life span. As the RM expires, the bank (lender) is entitled to lodge a claim on the discrepancy if the loan balance is greater than the house value with the insurance company (IC). Our contribution is threefold. First of all, we use the Taiwan Life Expectancy Database and simulated house prices and interest rates from stochastic processes to estimate the constant annuity and the maximum loan to value. Secondly, we build a simulation model for insurance premium rates, which are charged by the IC to the lender and determined under the condition where the present value of expected claim losses is equal to that of the insurance premiums. Finally, we analyze the impact of the disposition time of RM collateral on insurance premiums based on our simulation results. Our paper can shed light on the implementation and further development of reverse mortgage plans in Taiwan.