IG-GARJI模型下之住宅抵押貸款保險評價

Abstract

住宅抵押貸款保險(Mortgage Insurance)為管理違約風險的重要工具，在2008年次級房貸風暴後更加受到金融機構的關注。為了能更準確且更有效率的預測房價及合理評價住宅抵押貸款保險，本文延續Christoffersen, Heston and Jacobs (2006)對股票報酬率的研究，提出新的GARCH模型，利用Inverse Gaussian分配取代常態分配來捕捉房價序列中存在的自我相關以及典型現象(stylized facts)，並且同時考慮房價市場中所隱含的價格跳躍現象。本文將新模型命名為IG-GARJI模型，以便和傳統GARCH模型作區分。由於傳統的GARCH模型在計算保險價格時，通常不存在封閉解，必須藉由模擬的方法來計算價格，會增加預測的誤差，本文提供IG-GARJI模型半封閉解以增進預測效率與準確度，並利用Bühlmann et al. (1996)提出的Esscher transform方法找出其風險中立機率測度，而後運用Heston and Nandi (2000)提出之遞迴方法，找出適合的住宅抵押貸款保險評價模型。實證結果顯示，在新建房屋市場中，使用Inverse Gaussian分配會比常態分配的表現要好；對於非新建房屋，不同模型間沒有顯著的差異。另外，本文亦引用Bardhan, Karapandža, and Urošević (2006)的觀點，利用不同評價模型來比較若房屋所有權無法及時轉換時，對住宅抵押貸款保險價格帶來的影響，為住宅抵押貸款保險提供更準確的評價方法。

Mortgage insurance products represent an attractive alternative for managing default risk. After the subprime crisis in 2008, more and more financial institutions have paid highly attention on the credit risk and default risk in mortgage market. For the purpose of giving a more accurate and more efficient model in forecasting the house price and evaluate mortgage insurance contracts properly, we follow Christoffersen, Heston and Jacobs (2006) approach to propose a new GARCH model with Inverse Gaussian innovation instead of normal distribution which is capable of capturing the auto-correlated characteristic as well as the stylized facts revealed in house price series. In addition, we consider the jump risk within the model, which is widely discussed in the house market. In order to separate our new model from traditional GARCH model, we named our model IG-GARJI model. Generally, traditional GARCH model do not exist an analytical solution, it may increase the prediction error with respect to the simulation procedure for evaluating mortgage insurance. We propose a semi-analytical solution of our model to enhance the efficiency and accuracy. Furthermore, our approach is implemented the Esscher transform introduced by Bühlmann et al. (1996) to identify a martingale measure. Then use the recursive procedure proposed by Heston and Nandi (2000) to evaluate the mortgage insurance contract. The empirical results indicate that the model with Inverse Gaussian distribution gives better performance than the model with normal distribution in newly-built house market and we could not find any significant difference between each model in previously occupied house market. Moreover, we follow Bardhan, Karapandža, and Urošević (2006) approach to investigate the impact on the mortgage insurance premium due to the legal efficiency. Our model gives another alternative to value the mortgage contracts.