Abstract
We develop a new type of contingent capital, called contingent convertible security (CCS), which is like a contingent convertible bond (CCB) but dier- ently can be interconverted repeatedly and automatically between debt and equity depending on two specied levels of the cash ow generated by the �rm that issues the CCS. We derive closed-form expressions of the equilib- rium prices of corporate securities and optimal capital structure when the cash ow of therm is modeled as geometric Brownian motion. Especially, we provide very simple formulas on optimal capital structure including a CCB. We show that the CCS can not only decrease default risk like a CCB, but also can signicantly increase therm's value. In particular, the CCS can be used to solvenancing problems of small- and medium-sized enterprises as well as banks.
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