Alternative Models for Evaluating Convertible Bond: Review and Integration

Abstract

This work reviews the literature on convertible debt valuation with various assumptions regarding the firm’s market value (or stock price) and interest rate (or straight bond’s price). For deterministic stock price and interest rate, the graphical method by Brigham (J Finance 21:35–54, 1966) is a representative. For stochastic variables, the valuation model can be further divided into static and dynamic depending on the valuation is for some known date or for some period of time in the future: the calculus models proposed by Baumol, Malkiel, and Quandt (Q J Econ 80:48–60, 1960), Poensgen (Indust Manage Rev 7:76–92, 1965, Industrial Manage Rev 7:83–88, 1966), and Frankel and Hawkins (J Finance 30:207–210, 1975) are representatives of the static stochastic models. While the dynamic stochastic models can be further divided into structural models and reduced-form models, respectively. For the structural models, Brennan and Schwartz (J Finance 32:1699–1716, 1977, J Financ Quantitat Analysis 15(4):907–929, 1980) and Ingersoll (J Financ Econ 4:289–321, 1977a; J Finance 2:463–478, 1977b) are the pioneers, in which the firm’s market value is assumed to follow a geometric Brownian motion. The more recent literature develop reduced-form models using stochastic stock price instead of firm’s market value for the underlying of the convertibles. These include the works by McConnell and Schwartz (1986), Goldman Sachs (Valuing convertible bonds as derivatives. Technical report, Goldman Sachs. Quantitative Strategies Research Notes, 1994), Ho and Pfeffer (Financ Analysts J 52:35–44, 1996), Tsiveriotis and Fernandes (J Fixed Income 8(2):95–102, 1998), Davis and Lischka (Convertible bonds with market risk and credit default. Working paper, Tokyo Mitsubishi International Plc, 1999), and Hull (2000).