An Uncertain Volatility Explanation for Delayed Calls of Convertible Bonds

Arbitrage-free price bounds for convertible bonds are obtained assuming a stochastic volatility process for the common stock that lies within a band but makes few other assumptions about volatility dynamics. Equity-linked hazard rates, stochastic interest rates and different assumptions about default and recovery behavior are accommodated within this approach. A non-linear multi-factor reduced-form equity-linked default model leads to a set of non-linear partial differential complementarity equations that are governed by the volatility path. Empirical results focus on call notice period effects, showing that uncertain volatility can capture the call premia so often observed in issuer's call policies. Increasingly pessimistic values for the issuer's substitution asset obtain as we introduce more uncertainty during the notice period. Volatility uncertainty is thus a useful mechanism to explain issuers delayed call policies.