Calibration and implementation of convertible bond models

Abstract

While convertible bond models recently have come to rest on solid theoretical foundation, issues in model calibration and numerical implementation still remain. This paper highlights and quantifies a number of such issues, demonstrating, among other things, that naïve calibration approaches can lead to highly significant pricing biases. We suggest a number of techniques to resolve such biases. In particular, we demonstrate how applications of the Fokker–Planck PDE allows for efficient joint calibration to debt and option markets, and also discuss volatility smile effects and the derivation of forward PDEs to embed such information into model calibration. Throughout, we rely on modern finite-difference techniques, rather than the binomial or trinomial trees that so far have dominated much of the literature.