Valuation of Callable Convertible Bond With Parisian Feature Using Finite Element Method

Abstract

To protect the conversion privilege from being called away too soon, the bond indenture commonly contains hard call constraint and soft call constraint, which makes the valuation for the convertible bond more complicated. In this paper, a valuation model for a callable convertible bond with Parisian feature and notice period requirement is presented here using the arbitrage-free valuation method. Different from the existing works, we analyze the interaction between the optimal call policy and the optimal conversion policy based on the game theory analysis of options. Moreover, the finite element method is adopted to solving the pricing model and the projected successive over-relaxation technique is used to handling the American constraint. Finally, the convertible bond issued by China Merchants Bank is taken for an example to illustrate how the model works. Results show that notice period and Parisian feature have significant effect on the value of convertible bond and the optimal policies, and the so called "delayed call" phenomena has got some explanations here.

Keywords: Convertible Bond, Parisian Option, Game Theory Analysis of Options, Finite Element Method

JEL Classification: C63, G13