Credit Risk: Pricing, Measurement, and Management

By David Lando | Go to book overview

2
Corporate Liabilities as Contingent Claims

2.1 Introduction

This chapter reviews the valuation of corporate debt in a perfect market setting where the machinery of option pricing can be brought to use. The starting point of the models is to take as given the evolution of the market value of a firm’s assets and to view all corporate securities as contingent claims on these assets. This approach dates back to Black and Scholes (1973) and Merton (1974) and it remains the key reference point for the theory of defaultable bond pricing.

Since these works appeared, the option-pricing machinery has expanded significantly. We now have a rich collection of models with more complicated asset price dynamics, with interest-rate-sensitive underlying assets, and with highly pathdependent option payoff profiles. Some of this progress will be used below to build a basic arsenal of models. However, the main focus is not to give a complete catalogue of the option-pricing models and explore their implications for pricing corporate bonds. Rather, the goal is to consider some special problems and questions which arise when using the machinery to price corporate debt.

First of all, the extent to which owners of firms may use asset sales to finance coupon payments on debt is essential to the pricing of corporate bonds. This is closely related to specifying what triggers default in models where default is assumed to be a possibility at all times. While ordinary barrier options have barriers which are stipulated in the contract, the barrier at which a company defaults is typically a modeling problem when looking at corporate bonds.

Second, while we know the current liability structure of a firm, it is not clear that it will remain constant in the remaining life of the corporate debt that we are trying to model. In classical option pricing, the issuing of other options on the same underlying security is usually ignored, since these are not liabilities issued by the same firm that issued the stock. Of course, the future capital-structure choice of a firm also influences the future path of the firm’s equity price and therefore has an effect on equity options as well. Typically, however, the future capital-structure changes are subsumed as part of the dynamics of the stock. Here, when considering

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