BFS 2002

Contributed Talk

This paper explores derivative security valuation when the underlying price process is controlled. Our particular application is valuing defaultable debt when the process for firm value is controlled by the firm's manager. Specifically, the manager uses forward contracts to control (continuously) the firm's net investment in a risky technology. It is assumed that the manger has an incentive compensation contract based on firm value and seeks to maximize the expected utility associated with that compensation. Via a state variable transformation, we are able to generate analytic solutions for this control problem. That allows us to examine the effect on default probabilities and bond pricing of altering key parameters such as volatility and the degree of managerial risk aversion. We also compare the situation with and without managerial control, and provide insights on the relative benefits for lenders. Over and above the specific results for defaultable debt, our basic methodology appears broadly applicable to valuing payoffs on portfolios where the investment allocation is subject to managerial control.