BFS 2002

Contributed Talk

Two-Factor Convertible Bonds Valuation Using the Method of Characteristics / Finite Elements

Ana Bermudez, John Hatgioannides, Giovanni Barone-Adesi

In this paper we solve a two-factor convertible bonds model that fits the observed term structure, calibrates the volatility parameters to market data and allows for correlation between the state variables. We propose the Method of Characteristics together with Finite Elements for time and space discretization. Compared with the traditionally used numerical schemes of finite differences and lattices, our methodology offers clear advantages for solving two-dimensional problems in terms of flexibility in incorporating a number of final, boundary and jump conditions, generality to pricing a wide array of exotic two-colored options and accuracy. An empirical investigation into the pricing of National Grid Group's convertible issue produced prediction errors of less than 5\% for 215 successive trading days, a clear indication for commercially-usable and confident valuation of convertible bonds.