The market for convertible bonds has been expanding rapidly. In the U.S., over $105 billion of new convertibles were issued in 2001, as compared with just over $60 billion in 2000. As of early in 2002, there were about $270 billion of convertibles outstanding, more than double the level of five years previously, and the global market for convertibles exceeded $500 billion.1 Moreover, in the past couple of decades there has been considerable innovation in the contractual features of convertibles. Examples include liquid yield option notes (McConnell and Schwartz, 1986), mandatory convertibles (Arzac, 1997), “death spiral” convertibles (Hillion and Vermaelen, 2001), and cross currency convertibles (Yigitbasioglu, 2001). It is now common for convertibles to feature exotic and complicated features, such as trigger prices and “soft call” provisions. These preclude the issuer from exercising its call option unless the firm’s stock price is either above some specified level, has remained above a level for a specified period of time (e.g. 30 days), or has been above a level for some specified fraction of time (e.g. 20 out of the last 30 days).
The modern academic literature on the valuation of convertibles began with the papers of Ingersoll (1977) and Brennan and Schwartz (1977, 1980). These authors build on the “structural” approach for valuing risky non-convertible debt (e.g. Merton, 1974; Black and Cox, 1976; Longstaff and Schwartz, 1995). In this approach, the basic underlying state variable is the value of the issuing firm. The firm’s debt and equity are claims contingent on the firm’s value, and options on its debt and equity are compound options on this variable. In general terms, default occurs when the firm’s value becomes sufficiently low that it is unable to meet its financial obligations.2 An overview of this type of model is provided in Nyborg (1996). While in principle this is an attractive framework, it is subject to the same criticisms that have been applied to the valuation of risky debt by Jarrow and Turnbull (1995). In particular, because the value of the firm is not a traded asset, parameter estimation is difficult. Also, any other liabilities which are more senior than the convertible must be simultaneously valued.