2019年底所爆發的新型冠狀病毒疫情對於全球經濟帶來重大的影響，人們的消費模式及活動受病毒肆虐的影響，出現了改變及限制；企業經營的風險和對於未來的不確定性大幅上升。在本研究中，我們想藉此觀察美國上市公司於疫情期間，破產的可能性以及公司股價預測之機率密度函數的捕捉及變化。

兩種模型，分別為混合對數常態分配模型搭配破產機率（Mixture Lognormal Densities with Probability of Bankruptcy ，MLNbk）以及正卷積近似模型（Positive Convolution Approximation，PCA）將被採用，並藉由股票選擇權價格所隱含著市場參與者對於未來預期的特性，本研究透過股票選擇權價格來協助估計公司之隱含破產機率以及捕捉風險中立機率密度函數圖形。我們比較及檢視兩模型之配適結果，並特別觀察擁有估計之高隱含破產機率的日期，其機率密度函數的變化以及所可能反應於市場上的相對事件。

The outbreak of Coronavirus at the end of 2019 has brought significant impact to the global economy. Consuming behavior patterns of customers and regular activities have been changed and restricted due to easily and quickly spread of virus. Business operations suffered terribly and the risk undertake by the company and the uncertainty of the future has risen. In this study, we would like to estimate the implied bankruptcy probability and examine the shape of risk neutral density during this period of time.

Two models, Mixture Lognormal Densities with Probability of Bankruptcy (MLNbk) and Positive Convolution Approximation (PCA) are applied. Owning to the characteristics of stock option prices which contain the information about market participants’ expectations for the future, stock option prices of United States listed companies are used to estimate the implied bankruptcy probability and the risk neutral density. We compared and examined the results between two models particularly on high implied bankruptcy probability dates to observe whether there are major events happen around that time.

第一章、前言 1
第二章、文獻探討 3
第三章、資料 6
第四章、研究方法 8
第一節、混合對數常態分配模型搭配破產機率
（Mixture Lognormal with Bankruptcy Probability，MLNbk） 8
第二節、正卷積近似模型（Positive Convolution Approximation，PCA） 10
第五章、實證結果 13
第六章、結論 27
附錄 28
參考文獻 30

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