Convertible bond pricing with partial integro-differential equation model

Abstract

In this paper, we introduce the concept of Exponential Variance Gamma (EVG) model to the valuation of convertible bond (CB). Rather than evaluating derivatives with standard Black–Scholes approach, we describe the dynamic underlying asset log price with VG process, which is one of classical Lévy processes with non-normal distribution but skewness and leptokurtosis. For numerical purpose, we develop a discrete scheme with stability and convergence, which combines so-called multi-stage compound-option model (MCO) and explicit–implicit difference method (EXIM) to discretize the partial integro-differential equation (PIDE). By comparing our results with Black–Scholes approach, we can show that because of the ability to capture skewness and leptokurtosis features, the new approach does provide a lower price for the valuation of CB.