Utility-Based Pricing of Contingent Convertible Bonds and Optimal Capital Structure

Abstract

We consider the utility-based pricing of corporate securities and optimal capital structure including contingent convertible bond (CCB). We derive the semi-closed-form solutions of the implied values of corporate securities without bankruptcy costs and taxes. Our numerical simulations show that CCB is able to increase the value of the issued firm while it also leads to a less bankruptcy risk. The higher the business risk or the more risk-averse the buyers are, the more (less) the CCB (straight bond) should be issued. Our model explicitly finds that a straight bond will decrease the implied value of equity by strengthening precautionary savings motive of the equity holder, but on the contrary, CCB will increase the implied value by weakening this motive. This is a hidden merit of CCB, which is overlooked in a risk-neutral world.

Keywords: Contingent convertible Bond, Capital structure, Consumption utility-based indifference pricing

JEL Classification: G12, G32