本研究目的在於對上市公司的隱含違約機率進行估計，進而預測公司違約可能性。我們利用混合對數模型來對厚尾機率(違約部分)進行捕捉，故可較為精確得估計隱含違約機率。為達此研究目的，本研究以OptionMetrics資料庫的31家破產公司為研究對象，研究各公司破產前三個月內的每日違約機率。我們採用最小平方法，將市場之選擇權價格與本研究推導出的選擇權理論價格，配適出模型參數，進而估計隱含違約機率。

為了解模型所獲得之隱含違約機率是否準確，我們不只研究破產公司的違約機率，亦挑選至今仍健在的公司作為對照組，以檢驗模型的預測能力是否精準。我們另以CAP方法，將研究數據與CDS所得出之違約機率做比較。另外，將兩種模型各自對違約公司與對照組做T檢定，以此檢驗此兩種模型對違約是否有顯著區分能力。

關鍵字：價格密度函數、機率預測、選擇權市場、CDS、模型配適

The purpose of this study is to estimate the implied default probabilities for listed companies. And then we can forecast the possibility of companies default. We use the mixed lognormal model to capture the fat tail of probability (default part), so we can estimate the implied default probabilities more accurately. In this study, 31 bankrupt companies in OptionMetrics database were selected, and the daily probability of default was estimated by three months before the company went bankrupt.

We use the least squared pricing errors method to estimate the model parameters, and then compute the implied default probabilities. In order to understand the accuracy of the implied probability of default obtained by this research model, we not only study the default probability of the bankrupt company, but also select a few companies that are still strong to determine whether the prediction ability of the model is great. We also compared our model to CDs by CAP. Besides, We do T test -for our model and CDS estimation method separately to understand whether they can distinguish default companies from the non-default counterparts.

Key word: pricing density function, probability prediction, option market, CDS, model matching

封面-----------------------------------------------------------
摘要----------------------------------------------------------1
致謝辭--------------------------------------------------------3
目錄----------------------------------------------------------4
第一章 前言---------------------------------------------------5
第二章 研究方法與步驟-----------------------------------------8
第三章 資料範圍與限制----------------------------------------13
第四章 實證結果----------------------------------------------17
第五章 與CDS比較--------------------------------------------24
第六章 結論--------------------------------------------------28
未來研究方向-------------------------------------------------29
附錄---------------------------------------------------------30
參考文獻-----------------------------------------------------36

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