Electronic Thesis and Dissertation Repository

Degree

Doctor of Philosophy

Program

Applied Mathematics

Supervisor

R. Mark Reesor

2nd Supervisor

Adam Metzler

Joint Supervisor

Abstract

A contingent capital bond (CCB) is a subordinated security that converts to common shares when a predetermined trigger is breached. The 2008 financial crisis and the Basel III motivate the issuance of CCBs, aiming to mitigate the too-big-to-fail problem in financial distress and to resolve financial institutions by bailing in with the firm’s own capital rather than a bailing out using the taxpayers’ money.

Within the structural modelling framework, we consider the pricing of CCBs with an affine geometric Brownian motion by assuming that coupon payments have impact on the asset value dynamics. We extend the capital structure into four tranches including deposits, equity, and senior and subordinated bonds, and calibrate the model to Canadian banking data. Under infinite maturity, we derive a closed-form formula to price CCBs. Regulatory suggestions can be made based on our model in the design of conversion terms in recognition to the creditor- claim seniority and to ensure that equity investors are not rewarded for poor performance. Under the finite-maturity case, the term structures of CCBs are investigated by applying Monte Carlo simulation.

When the conversion price is based on the contemporary market stock price (as it tends to be in practice), CCB investors may have incentives to short the firm’s stock to depress the market stock price and earn favourable returns from possible future conversion. Continuing with the structural model, we allow for a deviation between the stock’s fundamental value and market value and use it to analyze the CCB investors’ incentives to short. We discuss three kinds of market-based conversion prices and find that directly using the contemporary market stock price could tempt manipulations. However, adding a floor to the contemporary market stock price or using the trailing average instead would curb the manipulation incentives.

Among the issuances of CCBs, one noticeable characteristic is that regulators retain the right to force the conversion in view of the issuing firm’s solvency prospects and the economic stability. In an intensity-model based approach, we incorporate regulatory discretion into the pricing model and therefore manage to quantify the impact of regulatory uncertainty on the cost of CCBs. Reasonable intervals for conversion terms are also detected under the regulatory trig- ger. Two categories of intensity functions are considered to distinguish regulators’ behaviours towards non-systemically important and too-big-to-fail financial institutions. In general, the CCBs issued by too-big-to-fail financial institutions are more expensive than those issued by non-systemically important financial institutions due to the feature that conversion is sure to happen before liquidation.

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