Most of the existing literature on option pricing takes the stock price process as exogenously given. Viewing equity
as an option on firm value, it is possible to endogenize the stock price process. These so-called "structural credit
risk models" have been used primarily for the valuation of debt and credit derivatives. In this book, however, we
take a look at the implications of this approach for the pricing of equity options.
Following a description of the main economic ideas and an introduction to some of the techniques needed in later
parts of the book (in particular, the martingale pricing approach and numeraire change), we give a brief review of
some exotic options which will double as building blocks in more complicated models. We describe a firm value
based security pricing framework recently proposed by Ericsson/Reneby (1998), and show how a number of well-
known structural credit risk models can be conveniently re-derived within this framework. This framework has two
main advantages compared to the "classical" PDE approach: First, economic interpretation of the resulting
formulae is greatly simplified. Second, derivation of pricing formulae for options on corporate securities becomes
straightforward.
The main idea, again first described by Ericsson/Reneby (1996), is presented, and some necessary corrections to
their result are made. Then, by deriving pricing formulae for an array of additional claims, the applicability of this
option pricing framework is greatly widened. This is demonstrated both by recasting some existing results in terms
of this framework, and by deriving pricing formulae for equity options within a number of additional structural
credit risk models.
Numerical results illustrate the implications of pricing equity options using an endogenous stock price process. We
find that, e.g., firm value based option pricing models may explain the "volatility smile" observed in options
markets. Numerous figures and tables allow for an easy comparison of various structural credit risk models of all
degrees of sophistication. A summary and some directions for further research conclude.