本研究目的在於通過正卷積近似模型(Positive Convolution Approximation Model, PCA model)，使用選擇權資料估計美國上市公司的隱含破產機率，進而預測公司破產的可能性。收集美股市場中申請破產保護，並且擁有選擇權資料的公司，通過PCA模型去預測未來股價分布，並以歷史數據為參考計算破產機率。接著使用公司內幕股票交易資料，將其整理後成為不同的內幕股票交易變數。通過羅吉斯回歸模型，觀察加入內幕股票交易變數後，是否提升模型預測破產事件的準確度，並檢視個別內幕股票交易變數對破產事件之解釋力。

實證結果顯示大部分破產公司通過 PCA 模型估計出的破產機率是顯著大於非破產公司的，但仍有接近三分之一的破產公司未顯著大於非破產公司，可見 PCA 模型及參考資料都還有待優化。而內幕股票交易實證顯示，整理出的內幕股票交易變數對於破產事件本身並未有顯著的解釋力，整體模型的預測準確率也只有微幅提升。總結來說，內幕股票交易資訊並沒有給出很好的破產事件解釋力。

The study aims is to estimate the implied bankruptcy probability by the option data of 72 U.S. listed companies from 2016 to 2020 with positive convolution approximation (PCA) model. Further, we want to predict whether these companies go bankrupt. Firstly, we collect information on companies in the US stock market that have filed for bankruptcy protection and have option data. Then we use the PCA model to estimate the future stock price distribution. Finally, we can use historical data as a reference to calculate the probability of bankruptcy. Secondly, we use company insider stock trading data to build a variety of insider stock trading variables. Using the Logistic regression model, we observe whether adding insider stock trading variables improves the model's accuracy in predicting bankruptcy events. Also, we examine the explanatory power of individual insider stock trading variables for bankruptcy events.

The empirical results show that the bankruptcy probability estimated by the PCA model of most bankrupt companies is significantly greater than that of non-bankrupt companies. However, there are still nearly one-third of bankrupt companies are not significantly larger than non-bankrupt companies. It can be seen that the PCA model and reference data still need to be optimized. Furthermore, The insider stock trading empirical evidence shows that the insider stock trading variables have no significant explanatory power for the bankruptcy event. And the prediction accuracy of the overall model has only slightly improved. Therefore, the insider stock trading information is not given a very good explanation for bankruptcy events.

摘要 i
Abstract ii
第一章 緒論 1
第二章 文獻回顧 4
第三章 資料 7
第四章 模型設定 12
第五章 實證分析 17
第六章 結論 28
附錄圖一、各家公司從PCA估計出的隱含破產機率時間序列圖 30
附錄表一、內幕股票交易資料變數彙整 36
參考文獻 39

中文文獻
1. 劉學謙 (2010). ” 密度函數預測績效的比較分析 -以英國富時指數 100 為例” 國立清華大學計量財務金融系碩士論文.
2. 劉姿伶 (2020). ” 隱含破產機率之研究－ 以新冠肺炎中後期間美國上市公司為例” 國立清華大學計量財務金融系碩士論文.
3. 許文昌 (2019). ” 隱含違約機率之研究” 國立清華大學計量財務金融系碩士論文.
4. 李柏嶔 (2016). ” 選擇權評價模式預測公司破產之研究” 國立清華大學計量財務金融系碩士論文.

英文文獻
1. Anand, Chakravarty (2007). ” Stealth trading in options markets” Journal of Financial and Quantitative Analysis. 42 (1), 167-1188.
2. Bakshi, Ca and Chen (1997). ” Empirical performance of alternative option pricing models” Journal of Finance . Vol. LII, NO. 5 . 2003-2049.
3. Beneish, Press and Vargus (2012). ” Insider trading and earnings management in distressed firms” Contemporary Accounting Research Vol. 29 No. 1 , 191-220.
4. Bernales, Verousis, Voukelatos, Zhang (2020). ” What do we know about individual equity options?” Journal of Futures Markets.40:67–91
5. Bondarenko (2003). ”Estimation of risk-neutral densities using positive convolution approximation” Journal of Econometrics. Volume 116, Issues 1–2, 85-112.
6. Breeden and Litzenberger (1978). ” Prices of State-contingent Claims Implicit in Option Prices” The Journal of Business , Oct., 1978, Vol. 51, No. 4 (Oct., 1978), pp. 621-651
7. Câmara, Popova and Simkins(2012). ” A comparative study of the probability of default for global financial firms” Journal of Banking & Finance Volume 36, Issue 3, March 2012, Pages 717-732
8. Chen, Martin and Wang (2013). ” Extraction of lignocellulose and synthesis of porous silica nanoparticles from rice husks: a comprehensive utilization of rice husk biomass” ACS Sustainable Chem. Eng. 2013, 1, 2, 254–259
9. Diltz and Kim (1996). ”The Relationship Between Stock and Option Price Changes” The financial review Vol.31, No.3(Aug., 1996), pp. 499-519
10. Ge, Hu, Humphery-Jenner and Lin (2019). “Informed Options Trading Prior to Bankruptcy Filings” Research Collection Lee Kong Chian School Of Business. 1-47.
11. Hao, Lee and Piqueira (2013). ” Short Sales and Put Options: Where is the Bad News First Traded?” Journal of Financial Markets 16 (2013) 308–330
12. Iqbal, Shetty (2002). ” An investigation of causality between insider transactions and stock returns” The Quarterly Review of Economics and Finance 42 (2002) 41–57
13. Lu (2019). ” Monte Carlo analysis of methods for extracting risk‐neutral densities with affine jump diffusions” J Futures Markets. 2019;39:1587–1612.
14. Merton (1974) . ”On the Pricing of Corporate Debt: The Risk Structure of Interest Rates” Journal of Finance. 29 (2), 449-470.
15. Poteshman (2006) . ” Unusual option market activity and the terrorist attacks of September 11, 2001” The Journal of Business , Vol. 79, No. 4 (July 2006), pp. 1703-1726
16. Seyhun and Bradley (1997). ” Corporate bankruptcy and insider trading” The Journal of Business , Vol. 70, No. 2 (April 1997), pp. 189-216
17. Truong (2012). ” Options trading and the extent that stock prices lead future earnings information” Journal of Business Finance and Accounting 39 (7-8), 960–996.
18. Taylor, Tzeng and Widdicks (2014). ” Bankruptcy probabilities inferred from option prices” The Journal of Derivatives Winter 2014, 22 (2) 8-31.