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Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematics

Program Name/Specialization

Mathematics for Science and Finance

Faculty/School

Faculty of Science

First Advisor

Mark Reesor

Advisor Role

Supervise

Second Advisor

Adam Metzler

Advisor Role

Supervise

Abstract

The 2007-09 financial crisis showed financial institutions are vulnerable during distressed times. As an alternative resolution to a government bail-out, contingent convertible securities (contingent capital or CoCos) were proposed by various researchers. CoCo is a hybrid capital security that converts from a bond to common equity when a pre-determined event occurs. The loss absorption mechanism of CoCo is essential to the financial health of a bank during a crisis as it provides an instant capital infusion when public capital is difficult to access.

In this thesis, we first implement a methodology to calibrate capital structure models for large Canadian banks. Typical studies involving capital structure model calibration focus on non-financial firms as they have lower leverage. We calibrate unknown parameters to multiple market-observed quantities, where the asset value process allows for discontinuous jumps. From a theoretical perspective, we find that jumps in the asset-value process are necessary to obtain a satisfactory fit to market data.

We then include a stylized CoCo bond in a bank's capital structure and calibrate the conversion threshold using market data. We treat the conversion threshold level as an exogenous parameter to be calibrated. In practice, contingent capital conversion triggers are discretionary, and there is considerable uncertainty around when regulators are likely to enforce conversion. We use the market-implied conversion triggers to infer when the market expects regulators to enforce conversion. We find that the market expects regulators to enforce conversion while the issuing bank is a going concern, as opposed to a gone concern. This fact is presumably of interest to potential dealers, regulators, issuers, and investors.

A lower conversion price benefits CoCo holders as the number of shares they receive is inversely related to the conversion price. In situations where the conversion price is based on the market stock price, CoCo holders could benefit from an artificially lowered market stock price. We investigate whether short selling equity is profitable for CoCo investors. We assume the CoCo investors open a short position on the bank's stocks when they perceive that conversion is imminent. Their return consists of two parts: (1) return from the additional shares received due to pushing the market share price below its fundamental value, and (2) return from price decline. Our results from the weighted average total returns and Sharpe ratios show that CoCo holders will not benefit from short selling equity unless they can time the market perfectly and are able to push the market stock price well below its fundamental value.

Convocation Year

2025

Convocation Season

Spring

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