Analytic Pricing of CoCo Bonds

We present a new model for pricing contingent convertible (CoCo) bonds which facilitates the calculation of equity, credit and interest rate risk sensitivities. We assume a lognormal equity process and a Hull–White (normal) short rate process for the conversion intensity with a downward jump in the equity price on conversion. We are able to derive an approximate solution in closed form based on the assumption that the conversion intensity volatility is asymptotically small. The simple first-order approximation is seen to be accurate for a wide range of market conditions, although particularly for longer maturities higher order terms in the asymptotic expansion may be needed