Pricing Convertible Bonds by Finite Element Method

Abstract

In this thesis, the proposed problem is to solve the system of two-coupled Black-Scholes equations, which is the so called TF (Tsiveriotis and Fernandes) model [16], for pricing the convertible bonds by the finite element method. Firstly, the derivation of the TF model is reviewed and introduced based on original work of Tsiveriotis and Fernandes [16]. Standard transformations are applied to the Black-Scholes equations to obtain a systemoftwoparabolicequations. Afterthetransformations, thefiniteelementmethod is introduced and is applied to solve the new system. The well-posedness of the method is discussed and numerical implementation of the schemes are presented. Finally, the some numerical examples by the finite element method are obtained.