原本只是單一地區的金融商品破局，但隨多米諾骨牌效應使之蔓延成為全球性流動與信用危機，而近年金融海嘯問題源頭錯綜複雜，其中之一可能性為定價衍生性金融商品時，錯估承受不可預期損失風險程度，使得定價過程即產生異常情況。

為量化此不可預期損失風險程度，則利用模擬房價與利率情況假設下，將影響住宅抵押貸款證券提前清償與違約的顯著變數納入考量，並將採用Calhoun and Deng (2002)文中所估計出來的影響因子係數，配合多元名義分對數模型(multinomial logit models)進而計算季頻之條件違約機率(Conditional Default Rate)與條件提前清償款率(Conditional Prepayment Rate)，計算累積損失率的分布狀況，配合各種情境分析下最適之違約損失率(Loss Given Default Rate)，進一步決定最適住宅抵押貸款證券各分券規模厚度，即可另外將原始住宅抵押貸款利息、本金償還與違約曝險金額之現金流量依據各分券所應承載之風險水準進行重組。

根據計算後分券規模，將住宅抵押貸款所產生的現金流量，包含各期應付利息、本金償付和違約回收金額正確導流至資產抵押證券中所屬分券，給定各分券合理之風險利差(Spread)，推求計算各分券投資者所隱含內部報酬率，利用夏普值(Sharpe ratio)判斷所承受的損失風險程度對應報酬率關係，發現各分券所呈現的夏普值並非水平線，表示在校準後的報酬出現異常現象，顯示在決定分券規模同時異常現象亦伴隨產生。

Pricing financial derivates is viewed as one of the problems causing the subprime storm. With the domino effect, the fallout from the subprime mortgage crisis has been spreading across the globe rapidly. It might be likely that the panic results from being misestimated the level of unexpected loss.

In order to calibrate the level of such risk, this research simulates the house price and also the short rates. Furthermore, the next step is to estimate quarterly conditional probabilities of default and prepayment with the multinomial logit models introduced by Calhoun and Deng (2002). More importantly, the survival model is utilized to gen-erate the distribution of cumulated default rate to ensure the thickness of each tranche within the ABS.

Based upon the estimated the distribution of the thickness for the ABS tranche, this study redirects the cash flow generating by the FRM to investigate the extent to which the degree of the burden risk with corresponding rate of return. Adopting the Sharpe measure to standardize between the internal rate of return and exploring risk. Eventually, the result of Sharpe measure of each tranche does not appear horizon con-dition. As soon as the thickness of each tranche is decided, the shape of Sharpe meas-ure of each tranche is certain. We observe an abnormal condition between return and risk of ABS.

Pennington-Cross,A.,G.Ho.(2006).”The Termination of Subprime Hybrid and Fixed Rate Mortgages.”Federal Reserve Bank of St. Louis, Working Paper.

Buist,H.,T.T.Yang.(1998).”Pricing the Competing Risks of Mortgage Default and Prepayment in Stochastic Metropolitan Economies,” Managerial Finance 24(9/10),110-128

Calhoun,C.A.,Y.Deng.(2002).”A dynamic analysis of fixed and adjustable rate mort-gage terminations,”Journal of Real Estate Finance Economics 24(1/2),9-33

Chan,K.C.,G. A.Karolyi,F.A.Longstaff and A.B.Sanders.(1992).”An Empirical Com-parison of Alternative Models of the Short-Term Interest Rate,”Journal of Finance 47(3),1209-1227

Chen,R.R.,T.L.Tyler Yang.(1995).”The Relevance of Interest Rate Processes in Pricing Mortgage-Backed Securities,”Journal of Housing Research 6(2),315-332

Chomsisengphet,S.,A.Pennington-Cross.(2006).”Subprime Refinancing Equity Ex-traction and Mortgage Termination,”Federal Reserve Bank of St. Louis, Working Pa-per

Collin-Dufresne,P.,J.P.Harding.(1999).”A Closed Form Formula for Valuing Mort-gages,”Journal of Real Estate Finance and Economics 19(2),133-146

Cox, J.C., J.E. Ingersoll and S. A.Ross.(1985).”A theory of the term structure of in-terest rates,”Econometrica 53(2), 385-407

Duffie,D.,N.G rleanu.(2001).”Risk and Valuation of Collateralized Debt Obliga-tions,”Financial Analysts Journal 57(1),41-59

Fabozzi,F.J.(2004).Bond Markets, Analysis, and Strategies. Pearson Prentice Hall

Gorton,G.(2008).”The Panic of 2007,” Yale School of Management, Working Paper

Greenlaw,D.,J.Hatzius,A.K. Kashyap and H.S.Shin.(2008).”Leveraged Losses: Les-sons from the Mortgage Market Meltdown,” U.S. Monetary Policy Forum ,Working Paper

Lin,C.C.,T.T.Yang.(2005).”Curtailment as a mortgage performance
indicator,”Journal of Housing Economics 14,294-314

Mason,J.R.,J.Rosner.(2007).”How Resilient Are Mortgage Backed Securities to Col-lateralized Debt Obligation Market Disruptions?,”Drexel University LeBow College of Business, Working Paper

Stephens,W.,Y.Li,V.Lekkas,J.Abraham,C.Calhoun andT.Kimner.(1995).”Conventional Mortgage Home Price Index,”Journal of Housing Research 6(3),389-418