In the multifaceted landscape of financial markets, the understanding and application of data science methods are crucial for achieving robustness, fairness, and strategic advancement. This dissertation addresses these critical areas through three interconnected studies.
The first study investigates the problem of data imbalance, with particular emphasis on financial applications such as credit risk assessment, where the prevalence of non-defaulting entities overshadows defaulting ones. Traditional classification models often falter under such imbalances, leading to biased predictions. By analyzing linear discriminant functions under conditions where one class's sample size grows indefinitely while the other remains fixed, this study reveals that certain parameters stabilize, providing robust predictions. This robustness ensures model reliability even in skewed data environments.
The second study explores anomalies in option pricing, specifically the total positivity of order 2 (TP₂) in call options and the reverse sign rule of order 2 (RR₂) in put options within the S&P 500 index. By examining the empirical significance and occurrence patterns of these violations, the research identifies potential trading opportunities. The findings demonstrate that while these conditions are mostly satisfied, violations can be strategically exploited for consistent positive returns, providing practical insights into profitable trading strategies.
The third study addresses the fairness of regulatory stress tests, which are crucial for assessing the capital adequacy of banks. The uniform application of stress test models across diverse banks raises concerns about fairness and accuracy. This study proposes a method to aggregate individual models into a common framework, balancing forecast accuracy and equitable treatment. The research demonstrates that estimating and discarding centered bank fixed effects leads to more reliable and fair stress test outcomes.
The conclusions of these studies highlight the importance of understanding the behavior of commonly used models in handling imbalanced data, the strategic exploitation of option pricing anomalies for profitable trading, and the need for fair regulatory practices to ensure financial stability. Together, these findings contribute to a deeper understanding of data science in finance, offering practical insights for regulators, financial institutions, and traders.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/y7e9-2r59 |
| Date | January 2024 |
| Creators | Li, Mike |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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