Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Applied Mathematics

Supervisor

Reesor, Mark

Abstract

My thesis includes three papers on contingent claims valuation of corporate securities using structural models of credit risk. Our study focuses on structural models and their applications in estimating damages in security class actions, option pricing and warrant pricing. Securities class actions typically involve some misrepresentation by a firm that overstates its true value. In securities class actions econometric models are used to assess damages to shareholders. However, studies on measuring damages for debt-holders are limited. My first paper uses a modified Merton framework to measure the impact of misrepresentation on the value of other components (e.g., debt, warrants) of a firm’s capital structure. Using structural models and leveraging the relationship between equity and firm value, we use observable eq- uity information to determine firm value and hence the effect of misrepresentation on value of other securities in the capital structure. We investigate various capital structures and show that misrepresentation can have a significant impact on the value of all components in the capital structure. We find that the misrepresentation impact on debt value depends on firm leverage and debt seniority and not on the warrant dilution factor. Generally, the debt for higher-leverage firms is more sensitive to the misrepresentation impact than for lower-leverage firms and junior debt is more affected by fraud than senior debt. The impact on warrant value is determined by warrant moneyness (stock price), with the dilution factor having no effect. My second paper extends the study in my first paper into the First Passage Time (FPT) framework, which is capable of modeling firms with complex debt structures. Our findings have important consequences for damages assessment and allocation of settlement awards in securities class actions. In some jurisdictions damages awarded are net of any hedge or risk- limitation transaction. Since corporate securities such as bonds and stocks are often held in portfolios for hedging purposes, measuring the effect of misrepresentation on all of the firm’s issuances is essential to accurately computed damages awards. In addition to our main findings, we explicitly discuss bankruptcy costs for the First Passage Time model. Furthermore, we are able to reduce a system of two non-linear equations, used to connect the unobservable firm value and firm value volatility to observable equity value and equity volatility, into one equation. This technique improves the ability to solve the non-linear system. My third paper studies option and warrant pricing under the structural framework (both Merton and FPT frameworks). We study the calibration of structural frameworks using a mar- ket implied volatility skew. We show that the model implied volatility skew under FPT frame- work is much more flexible than that under the Merton framework. Moreover, we extend the FPT structural framework to include warrants into the firm’s capital structure. Using historical market data, we show the pricing model (for both options and warrants) under FPT framework significantly outperforms the pricing models under Merton framework.

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