Pricing Contingent Convertible Bond with Idiosyncratic Risk

Under an incomplete market, we develop a utility-based pricing model for equity and contingent convertible bond (CCB) while the straight bond is priced by an equilibrium pricing method. We derive the semi-closed-form solutions of the utility-based prices of equity and CCB and the explicit equilibrium prices of all securities. We find that the increased firm value due to CCB increases dramatically with idiosyncratic risk volatility and risk aversion index. The firm value is a concave function of conversion ratio of CCB and there is a unique global maximum point. The optimal conversion ratio increases with the risk aversion index. If investors are risk-averse enough, as idiosyncratic risk rises, the optimal capital structure includes less CCB and equity but more straight bond. However, if investors are risk-neutral, the opposite holds true. In general, there are risk-taking incentives for risk-neutral investor but on the contrary, there are not even if investor is somewhat risk-averse. The higher the conversion ratio of CCB or the larger the risk aversion index, the weaker the risk-taking incentives but there is no obvious evidence on whether CCB will further decrease the risk-taking incentives