考量房價與利率關係的不動產逆向抵押貸款定價： 利用最大熵原則Pricing Reverse Mortgage under the Relationship between Housing Price and Interest Rate: Using the Principle of Maximum Entropy

本文利用Yilmaz & Selcuk-Kestel(2018)所發展之房價與利率模型，探討RM定價問題。與其它文獻不同，此模型房價與利率之間的關係，因當前利率大小而不同，此特性和傳統模型中相關性維持不變有所不同。另外本文說明如何利用最大熵原則(the principle of maximum entropy)，求解風險中立機率。此方法與其它求解風險中立機率的方法如Girsanov轉換相比，較為簡單。最後本文利用實證資料，分析不同參數對RM的影響。實證結果顯示，房價與利率之間的關係的確隨著當前利率大小而變動，而非固定維持正相關或負相關。本文也提供不同參數對RM年金的影響，供政府和貸方做為RM政策或年金制定時的參考方向。
關鍵詞：不動產逆向抵押貸款、風險中立機率、最大熵原則

ABSTRACT
This paper takes advantage of the model in Yilmaz & Selcuk-Kestel(2018), which accounts for housing prices and interest rates. The model is different from others that the relationship between housing prices and interest rates depends on the value of the current interest rate. In addition, this paper introduces how to derive a risk-neutral probability measure by means of the principle of maximum entropy. The technique is more mathematically tractable, which is different from other methods used to derive risk-neutral probability measures, such as the Girsanov’s transformation. Finally, empirical data is adopted to study the effects of different factors on the value of a RM. The empirical results show that the relationship between housing prices and interest rates indeed varies according to the value of the current interest rate, instead of maintaining positive or negative correlation. This paper also provides the effects of different factors on the annuity of RM, which contributes to policy decisions and determining annuities of RMs.
Key words: reverse mortgage, risk-neutral probability measure, the principle of maximum entropy