本文探討可違約互換率之匯率連動選擇權的評價，外國以及本國違約交 換率的動態是建立在LIBOR 市場模型的框架。為了簡化推導過程，我們將 原本本國以及外國交換率的雙動態轉為單一動態, 因此違約以及履約價將轉 換為一個固定的常數比率來評價可違約互換率之匯率連動選擇權。由於商品 本身是考量違約的情況，因此使用遠期的存活測度來評價可違約互換率之匯 率連動選擇權。最後在數值分析的部分我們使用蒙地卡羅來模擬可違約互換 率之匯率連動選擇權，理論值與模擬值的結果接近。 / This study prices quanto options on defaultable swap rates (QODSR) in which domestic and foreign defaultable swap rates are considered in the LIBOR market model. We use two fixed ratios to price the QODSR with the default and strike rate property. The forward default-swap measure provides a simple method for valuing the QODSR. Numerical analysis is performed and compared with the Monte Carlo method to investigate the effects of volatility and default on the QODSR.

本論文推導違約風險下四種新奇選擇權的評價模型及其避險比率，依序為數據選擇權、寬它選擇權、互換選擇權，極值選擇權。並比較無違約風險與違約風險下的評價模型之差異。假若違約風險不存在時，違約風險下各種類型選擇權的評價模型皆會縮減成為無違約風險下所對應的評價模型。避險比率亦為如此。數值範例則印證違約風險下選擇權的價值較無違約風險選擇權的價值低。本論文完成目前尚無任何學術研究於違約風險下四種新奇選擇權的評價模型及避險比率。這是一個重要貢獻。 關鍵詞：違約風險、新奇選擇權、數據選擇權、寬它選擇權、互換選擇權、極值選擇權。 / This paper presents the analytic pricing formula and the hedging ratio of four kinds of exotic options with correlated credit risk. They are Digital options, Quanto Options, Exchange Options and Extreme-value Options, respectively. Furthermore, compare the discrepancy of the models under the condition whether the default risk exists. Finding that if there is no default risk, all models that we derive will reduce to the corresponding models with no default risks, and so do the hedging ratio. Numerical examples certify that the value of the vulnerable options will be lower than that of the ordinary options. All above that finished has not been done by existing researches and it is a chief contribution in this paper. Keywords: Exotic Options, Credit Risk, Digital Options, Quanto Options, Exchange Options, Extreme-value Options, Default Risk.

房屋貸款保證保險制度可移轉部分違約風險予保險公司。然而，保險公司與金融機構在共同承擔風險之際，因房貸保證保險制度之施行，於提高貸款成數後，產生違約風險提高之矛盾現象；而估計保險之預期損失時，以目前尚無此制度下之違約數據估計損失額，將有錯估之可能。 本研究以二元邏吉斯特迴歸模型(Binary Logistic Regression Model)與存活分析(Survival Analysis)估計違約行為，並比較各模型間資料適合度及預測能力，進而單獨分析變數-貸款成數對違約率之邊際機率影響。以探討房貸保證保險施行後，因其對借款者信用增強而提高之貸款成數，所增加之違約風險。並評估金融機構因提高貸款成數後可能之違約風險變動，據以推估違約率數據，並根據房貸保證保險費率結構模型，計算可能之預期損失額，估算變動的保險費率。 實證結果發現，貸款成數與違約風險呈現顯著正相關，貸款成數增加，邊際影響呈遞增情形，違約率隨之遞增，而違約預期損失額亦同時上升。保險公司因預期損失額增加，為維持保費收入得以支付預期損失，其保險費率將明顯提升。故實施房屋貸款保證保險，因借款者信用增強而提高之貸款成數，將增加違約機率並對保險費率產生直接變動。 / Mortgage insurance system may transfer part of the default risk to insurance companies. However, the implementation of mortgage insurance system, on increasing loan to value ratio, the resulting increase default risk. And literatures estimate the expected loss without the default data, there will be misjudge. Our study constructs the binary logistic regression model and survival analysis to estimate the mortgage default behavior, and compare the data between the model fit and the predictive power. Analyzes the effect of loan to value ratio on the marginal probability of default rate. Furthermore, assess the financial institutions in the risk of default due to loan to value ratio changes. According to the estimated default rate data, we employ the mortgage insurance rate structural model to calculate the expected amount of loss and the changes in premium rates. Empirical results found loan to value ratio have a significant positive effect on borrowers’ default. Loan to value ratio increase, the marginal effect progressively increase, along with increasing default rates and expected default losses. Due to the ascendant expected loss, insurance companies increase premiums to cover the expected loss, the premium rate will be significantly improved. Therefore, the implementation of mortgage insurance, credit enhancement for the borrower to improve loan to value ratio, will increase the probability of default and insurance rates.

台灣早期有關系統風險（β）的研究皆指出β不能解釋台灣股票報酬的變異，故控尋更能解釋股票報酬的風險因素為本文的主要目的之一。 本研究分析民國71年7月至85年5月股票上市公司資料（排除金融、保險、及變更交易方式的公司）。因民國79年股價指數從2月的最高點12,495急遽下滑至10月的2,560，故分析上將79年度予以排除。在71年7月至78年12月的時段中，整體市場因素（RM-RF）不能解釋股票報酬的變異。此點發現與台灣早期研究的結論一致。其他變數顯著者僅有與規模有關的因素（SZSMB），或與負債比率有關的因素（DEHML），其中以 SZSMB的解釋能力最強。在民國80年1月至85年5月的時段中，所有模式中整體市場因素（ RM-RF）的係數皆顯著，並且是所有因素中最顯著者。這點發現與前時段（71年7月至78年12月）的結果有很大的不同。其他的變數顯著者，有代表成長機會的BMHML（與淨值市價比有關的因素）、EPHML（與益本比有關的因素）、或CPHML（與營運現金市價比有關的因素），及代表利率結構有關的風險因素TERM（與利率期間結構有關的風險溢酬）、或DFT（與利率違約風險有關的風險溢酬）。其中以（RM-RF）、EPHML、CPHML及TERM的風險組合最能解釋股票報酬的變異。 應用更完整的股票報酬解釋變數，探討股票報酬與盈餘間的關係，亦為本文主要目的之一。經分析以(1)各時段最能解釋股票報酬的因素組合為基礎，計算異常報酬；(2)單獨的以整體市場因素（RM-RF）為基礎計算異常報酬，然後再分別估出盈餘反應比較係數（ERC）比較之。結果顯示，以各時段最能顯著解釋股票報酬的因素組合為基礎的ERC為正的顯著，且其ERC大於只以整體市場因素（RM-RF）為基礎所算出的ERC。 另外，關於盈餘品質假說之測試，經以公司規模大小為虛擬變數放入迴歸式中，結果顯示，代表大公司的虛擬變數之係數時而為正，時而為負，且都不顯著，故盈餘品質假說未獲得支持。 再者，關於成長機會與ERC關係之測試，經以公司成長機會大小為虛擬變數放迴歸式中，結果顯示，代表成長機會的虛擬變數之系數時而為正，時而為負，且大都不顯著，故成長機會大的公司之ERC大於成長機會小的公司之ERC的假說，未獲得實證的支持。 / Earlier studies (Chen 1990; Chiu 1990; and Wang 1992) found that systematic risk (β) could not explain the variance of stock returns in Taiwan. The findings were inconsistent with the Capital Asset Pricing Model (CAPM). One of the major purposes of this paper is to examine the factors that have higher explanatory power of stock returns. To test the hypotheses, this study uses the data of Taiwanese listed companies covering the period from July 1982 to may 1996. The 1990 data are excluded because the stock market index climbed to a record high of 12,495 in February 1990 and then fell sharply to allow level of 2,560 in October 1990. The "crash" might cause structural changes in stock market, so the analyses are conducted separately for the periods before and after the crash, namely the prior-crash period (from July 1982 to December 1989) and the post-crash period (from January 1991 to May 1996). The empirical results show that for the prior-crash period the overall market factor (market returns minus risk free rate, RM-RF) can not explain the variance of stock returns. The findings are consistent with those of previous studies. However, we find that the factor-related to size (SZSMB) and the factor related to debt/equity ratio (DEHML) have significant association with stock returns. Furthermore, SZSMB has higher explanatory power. In contrast, the overall market factor is the most significant factor for the post-crash period. Other factors that are significant consisted of (1) proxies for growth opportunities, including book-to-market equity (BMHML), earnings/price ratio (EPHML), and cash flow/price ratio (CPHML), and (2) the factors related to interest structure, including term structure (TERM) and default risk (DFT). Among these factors, the set of RM-RF, EPHML, CPHML, and TERM explains the variance of stock returns most. Another purpose of this paper is to use the aforementioned findings to study the relationship between stock returns and earnings. The results show that the earnings response coefficients based on the most explanatory factor portfolio of each period are positive and significant, and are greater than those based on the traditional systematic risk (β). The tests for earnings quality hypothesis indicate that the coefficients of the dummy variable proxies for big companies are insignificant. The earnings quality hypothesis is not supported. The tests regarding the relationship between growth opportunities and earnings response coefficients show that the coefficients of the dummy variable proxies for high growth companies are unstable. The hypothesis that the earnings response coefficients of high growth companies are greater than those of low growth companies is not supported by empirical evidence.