VALUING CONVERTIBLE BONDS WITH A PRIORITY ISSUER CALL OPTION USING THE FINITE DIFFERENCE METHOD

VALUING CONVERTIBLE BONDS WITH A PRIORITY ISSUER CALL OPTION USING THE FINITE DIFFERENCE METHOD

This paper, to the best of the author's knowledge, is the first to propose an efficient finite-difference method (FDM) for valuing a convertible bond (CB) whose issuer call option has priority over the holder's conversion right. The study aims to establish a clear valuation framework for CBs in which the call dominates the conversion. When the call is exercised, the call's credit risk varies with the state of the underlying CB. To capture this feature, new intermediate conditions are introduced. The numerical scheme is based on the Tsiveriotis-Fernandes (TF) model, which formulates the CB value and its bond component as coupled equations. An implicit scheme is adopted to enhance the temporal flexibility. Furthermore, a linear boundary condition together with the projected successive over-relaxation (PSOR) technique is employed to handle the complex payoff structure arising from multiple early-exercise features. This approach ensures a stable and convergent numerical solution.