Credit Risk Modelling with Default-Triggered Acquisition
Authors: Cheung, W.
Conference: Department of Economics, University of CambridgeAbstract:
In this thesis, I propose that, given the opportunities for default-triggered acquisition (DTA), it is liquidation risk rather than just default risk that should really concern creditors, particularly senior debt investors.
DTA is an important market phenomenon with significant implications for credit risk, but is under-researched in the credit risk modelling literature. This thesis attempts to bridge the gap. It develops three diffusion-based models, one for risky bond pricing (Chapter 3), and two for the potential acquirers’ positions, i.e., the European type of option-to- acquire (Chapter 6), and the Quasi-American type (Chapter 7). Far from being three unrelated models, these models are developed to serve one common theme - credit risk modelling. My research will pursue the establishment of a risky bond pricing model under the assumption that DTA is a wise decision, as opposed to pre-default acquisition. This assumption is justified through an analysis of the Quasi-American-European spread. All models are implemented numerically in this thesis. The numerical results derived are intuitive. The following summarises the key models developed in this thesis:
The risky bond pricing model. Chapter 3 develops a structural model of the defaultable bond, taking into account the possibility that the borrowing firm might be acquired following a default. In this model, post-default acquisition is treated as an event triggered where the alternative valuation of the firm’s assets exceeds the failing firm’s value, and covers the acquisition costs (which are essentially the conceded debt liability). Analytical results are derived for situations where default time is assumed to be either fixed (as in Merton (1974)) or random (as in Black and Cox (1976)) and there are one or more alternative valuations. The implementation and numerical analysis of the model are presented in Chapters 4 and 5, respectively.
The European option-to-acquire model. Instead of modelling from the bond investors’ point of view, Chapter 6 analyses the DTA problem from the perspective of potential acquirers, and develops a structural model of their position, i.e., the European option-to- acquire, with analytical results. A comprehensive numerical comparative static analysis is also undertaken, which provides some insights for the Greeks of the real option.
The Quasi-American option-to-acquire model. The risky bond pricing model addresses the DTA issue under the assumption that acquisitions only take place at default. Chapter 7 aims to examine whether this assumption is viable or not. It considers pre-default acquisition opportunities leading from the extension of the European option to the corresponding Quasi-American option-to-acquire. Numerical results are derived for a comprehensive numerical comparative static analysis. The comparison of the European and Quasi-American positions sheds some light on the circumstances in which DTAs become important.