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.
2014. , 41 p.