考量房價跳躍風險下房屋抵押貸款保險之評價

Pricing Mortgage Insurance Contracts with Housing Prices Following Normal Tempered Stable Processes

王昭文(Chou-Wen Wang)

《風險管理學報》 12卷1期 (2010/05) Pp. 53-68

https://doi.org/10.30003/JRM.201005.0003

摘要

近年來金融風暴與次貸危機事件，均導致房屋價格劇烈變動，若假設房屋價格為幾何布朗運動將低估房價跳躍風險。因此，本研究在假設對數房屋價格服從常態調和穩態過程（Normal Tempered Stable Processes）下，推導出房屋抵押貸款保險合理保費。運用1986年1月至2008年6月之美國全國新屋價格每月報酬率，本研究發現常態調和穩態過程具有極佳的配適能力。此外，透過數值分析可知，其他條件不變下，假設房屋價格為幾何布朗運動將低估房屋抵押貸款保險合理保費。此外，不論運用常態調和穩態過程之特例VG模型（α = 0）或是NIG模型（α = 1/2），房屋抵押貸款保險之合理保費價值差異不高，故運用NTS模型之模型風險（Model Risk）較低。

關鍵字

Lévy過程 ； 常態調和穩態過程 ； 跳躍風險 ； 房屋抵押貸款保險

並列摘要

Recently, the real estate crises such as subprime mortgage crisis lead to the dramatic jumps in housing price processes. The geometric Brownian motion (BGM), therefore, may neglect the jump behavior inherent in the housing price processes. Assuming the housing price processes follow Normal Tempered Stable (NTS)processes, this study derives the pricing formula for mortgage insurance premiums, capturing important characteristics of abnormal shock events. Using the U.S. monthly national average new home returns from 1986 to 2008, we find that, compared with the BGM, the NTS process has a better good-of-fit. Finally, the BGM will underestimate the fair premiums of mortgage insurance when the housing price processes follow NTS processes. In addition, for different special cases of NTS processes such as VG or NIG models, their fair premiums are virtually the same, which means that the model risk based on NTS processes is trivial.

並列關鍵字

Lévy Processes ； Normal Tempered Stable Processes ； Jump Risk ； Mortgage Insurance Contracts

參考文獻

Bardhan, A.,Karapandza, R.,Urosevic, B.(2006).Valuing Mortgage Insurance Contracts in Emerging Market Economies.Journal of Real Estate Finance and Economics.32,9-20.

Barndorff-Nielsen, O. E.(1997).Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling.Scandinavian Journal of Statistics.24,1-14.

Barndorff-Nielsen, O.E.,Shephard, M.(2001).Normal Modified Stable Processes.Theory of Probability and Mathematical Statistics.65,1-19.

Canner, G. B.,Passmore, W.(1994).Private Mortgage Insurance.Federal Reserve Bulletin.9,883-899.

Carr P.,Madan, D.(1998).Option Valuation Using the Fast Fourier Transform.Journal of Computational Finance.2,61-73.