Sharp Analytical Lower Bounds for the Price of a Convertible Bond

Abstract

Analytical approximations for the price of a convertible bond within defaultable Markov diffusion models are derived in this article. Because convertible bond pricing requires time-consuming finite difference or tree pricing methods in general, such proxy formulas can help to calibrate model parameters more efficiently. The derivation is based on the idea of “Europeanizing” the American conversion option of the holder. Hence, the quality of the approximations stands and falls with the value of the early conversion premium. In practice, the latter is typically close to zero, which implies that the analytical lower bounds are incredibly sharp.