One of the most important government policies to support and satisfy financing needs for marginal enterprises or special sectors in economic system is to provide credit guarantee. In Taiwan, while Small and Medium Enterprise Credit Guarantee Fund of Taiwan (SMEG) had been established to help small and medium enterprises (SMEs) acquiring bank loans successfully by providing credit guarantee, there is still a need to set up an appropriate credit rating systems for SMEs. This research proposes three kinds of assessment models to the credit risks of SMEG. While Model one employs a firm¡¦s financial performance, substituting debt level and estimated asset value and volatility into the model to derive probability of default (PD). Model two and three utilize a firm¡¦s risk premium observed from the loan rate to estimate credit level. The former belongs to the application of structure-form approach in the credit risk management model, on the other hand, the latter is the reduced-form approach. On the structure-form approach, due to the difficulties in accessing SMEs¡¦ public trade information in Taiwan, we adopt the Private Firm Model developed by Moody's KMV Company. We had also improved this PD evaluation model by taking some peculiar operating characteristics of Taiwan¡¦s SMEs into consideration. On the reduced-form approach, we apply risk-neutral model to estimate a firm¡¦s PD, which then been utilizing to evaluate the expected value of subrogation payment in the case of default. This can further go deeper to calculate the guarantee fee of a loan. The processes used in this model is same as that of actuarial methodology being used to determine the premium of a term insurance. The three credit risk management models proposed in this research are designed to reflect the market information of a SME, and to the applicability of operating in real world case. The empirical results indicate they could adequately reflect the risk levels of the SMEs to a certain extent. We hope to provide the SMEG with a method of evaluating credit risk of SMEs to establish a fairer and more reasonable guarantee fee, and contribute in enhancing and managing credit guarantee mechanism in Taiwan.

房屋抵押貸款的評價，因為需考慮到貸款人的提前清償及違約風險造成現金流量之不確定性，決定房屋抵押貸款的價格比決定一般違約證券的價格更具困難度。因此，如何合理評估抵押貸款證券的價值實為一值得深入探討之課題，本文即針對此議題進行研究。傳統文獻在進行房屋抵押貸款的評價方法，主要可區分為兩種：結構模型(structural-form approach)及縮減式模型(reduced-form approach)。目前的文獻上，其評價的封閉解只存在於結構式模型，但在此模型下的評價，存在著違約與提前清償條件的設定問題，這將對評價的準確性造成很大的影響，在實務的應用上有一定的限制。再者，結構式模型在處理多變數且變數間具相關性的情況，存在一定的複雜性與困難度，而縮減式模型在此情況的處理上是較容易的。本研究將從縮減式模型的角度，引入 Jarrow (2001)的概念，在包含多重變數並考慮變數間相關係數之縮減模型下，進行房屋抵押貸款封閉解的推導。透過此方法可協助資產管理者從事投資組合配置最適化與避險策略的分析，亦期望能提供實務界一個更具可行性與效率性之房屋抵押貸款評價模型。 / Valuing mortgage-related securities is more complicated than valuing regular defaultable claims due to the borrower’s prepayment behavior as well as the possibility of default. In general, the methods that are applied to investigate mortgage value and termination risk can be divided into two categories: a structural-form approach and a reduced-form approach. Some researchers use a structural-form model to obtain the closed-form formulae for the mortgage value. With this method, however, it is difficult to identify the critical region of early exercise and deal with the situation including multivariable and their correlations correlation among variables. As an alternative, the reduced-form model developed in this study is able to value the mortgage without setting boundary conditions, and can thereby accurately handle the multi-dimensional space of correlated state variables. This study extends Jarrow’s (2001) model to examine mortgage valuations. The purpose of this article is to derive a closed-form solution of the mortgage valuation equation under a general reduced-form model that embeds relevant economic variables. This new approach enables portfolio managers to undertake sophisticated portfolio optimization and hedging analyses, and makes it possible to more accurately and efficiently value the complicated mortgage.