Valuation and Analysis of Contingent Convertible Securities with Jump Risk

Abstract

We examine a new type of contingent capital, called contingent convertible security (CCS), when the asset value of the issuing firm follows a jump-diffusion process. The merit of CCS is that it can dynamically adjust capital structure almost without incurring adjustment costs. We obtain closed-form expressions of the equilibrium prices of all corporate securities. Compared with a standard capital structure, CCS can lead to as much as a 9.5 percent increase in the issuing firm's value but the number declines to 5.7 percent if classical contingent convertible bond (CCB) is issued instead of CCS. The larger the investment risk, the more pronounced the advantage of CCS over straight bond and CCB. In our model, CCS does not suffer the debt overhang problem and shareholders have no risk-shifting incentive to increase the diffusive volatility of asset value, though they benefit from a higher jump risk.

Keywords: contingent capital, debt overhang, risk-taking incentive, jump risk

JEL Classification: G13, G32