我國指數型房貸抵押債權證券評價與利率敏感度分析

Abstract

房貸抵押債權證券屬固定收益證券的一種，評價固定收益證券需對未來利率走勢作適當的評析，而此牽涉到利率模型的應用，並且房貸抵押債權證券具有許多一般固定收益證券所沒有的性質包括分期攤還、提前還款以及Cap、Floor等多項勘入式選擇權，而這些性質除了會對房貸抵押債權證券價格造成影響外，在利率風險的控管上也會有顯著的影響；除了上述因素外，利率模型的差異對於評價以及利率風險衡量也有其決定性的影響；本文除探討利率模型在評價上的差異外，另藉由OAD的估算衡量相關的利率風險。 在利率模型部分選取包括Vasicek、CIR、Linear Drift CEV Diffusion等均衡利率模型，這三者之間主要差異在於其利率波動度的衡量上，而Vasicek以及CIR都是被套入(nested in)於Linear Drift CEV Diffusion模型內。本文藉由最大概度估計量的估計求得其模型參數值，而無風險市場利率與標的指數間關係以部分調整模型描述之；由評價結果發現在完全浮動(pure floater)下的房屋貸款由於提前還款效果與折現效果的交互作用使得這三者間在評價結果上沒有很大的差異、在有Cap限制下，增加相同幅度的利率波動度對OU造成較顯著的影響；接著由OAD的利率敏感度分析發現1)Cap變化與MBS價格呈正向關係、而與MBS利率敏感度呈反向關係2)Margin變化與MBS價格呈正向關係、而與MBS利率敏感度間成反向關係3)調整週期期間與MBS價格呈反向關係、與MBS利率敏感度呈正向關係4)Teaser rate與MBS價格呈反向關係、而與MBS利率敏感度在有Cap/Floor存在下為正向關係，但在pure floater情形下關係並不明顯；上述之各項利率敏感性衡量結果皆以Vasicek過程較CIR以及CEV過程為高。最後考慮不同標的指數間的利率敏感度差異顯示在完全浮動制度下的環境，越能即時反映市場利率狀況的標的指數其利率敏感性越低、但在狹窄的cap/floor限制時，此現象可能產生相反的結果。

Mortgage Backed Securities(MBS) is a kind of Fixed Income Securities, In order to valuate this kind of Securities, we must create related term structure of interest rate. Since other factors such as Amortization, Prepayment, Cap and Floor options which are absent in other general Fixed Income Securities also affect the MBS pricing and interest rate risk, In the MBS pricing process, We should take account of these factors. This article valuate adjustable rate MBS price and examine the interest rate sensitivities by comparing different equilibrium interest rate models which are difference in volatility assumption, They are OU、CIR and Linear Drift CEV Diffusion process. We use the maximum likelihood method to estimate the parameters of various interest rate models and use partial adjustment model to describes the relation between market interest rate and mortgage index, We find it in the pure floater circumstance there are no large difference in MBS valuation results among these three interest rate process, and through the option adjusted duration method we find that there are positive correlation between Cap and Margin with the MBS price, in contrast with these, there are negative correlation between adjustment period and Teaser rate with the MBS price. On the side of interest rate sensitivities analysis, all relative results are opposite to that the correlation between MBS price and factors we discuss above. Finally, we investigate the interest rate sensitivities of various mortgage indices which are difference in speed adjusted to market interest rate, we find that the different dynamics of the major ARM indices lead to significant variation in the interest rate sensitivities of loans based on different indices.