Convertible Bonds: a Qualitative and Numerical Analysis

Sammanfattning: A convertible bond is a nancial instrument which has both an equity part and a xed-income part. The pricing of nancial securities has for quite obvious reasons become extensively studied in the past decades. In this paper we study the Black-Scholes model, based on the equity value, where the equity is modelled by geometric brownian motion. We introduce the pricing of nancial securities in general by Partial Differential Equation (PDE) approach. We continue by studying the convertible bond with a call feature, which is a derivative of the stock price. Our model leads to a free boundary problem together with a parabolic partial differential equation. We also give some analytical results on uniqueness and monotonicity of the solutions. This paper ends with a numerical study of the solutions for different bond features.