Convertible Bond Pricing Models

Abstract

Abstract. Convertible bonds are an important segment of the corporate bond market, with worldwide outstandings approaching US$235 billion. Simple pricing models value a convertible bond as being equivalent to a straight bond with an embedded option that enables the bond holder to convert to a specific amount of common stock. The straight bond is subject to both interest rate and credit risk, whereas the option to convert is dependent on the underlying stock price, which exposes the convertible bond holder to equity risk. The complexity of these features means that convertible bonds tend to be treated casually in major derivatives and corporate finance textbooks. This paper presents a survey of the theoretical and empirical aspects of convertible bond pricing. The limitations of these studies are highlighted to identify those areas of research that may improve the valuation process and facilitate the application of these securities for corporate financing.

Mezzanine Financing Instruments in Comparison to the Classic Financing Sources

“…Convertible bond combines both the rights connected with holding of a classic bond and the rights to exchange this bond for another security of the given issuer (Batten, Khaw, & Young, 2013;Zhang, 2016). In view of the characteristics of mezzanine financial sources, convertible bonds are understood as bonds exchangeable for certain property securities, i.e.…”

A Refined Laplace-Carson Transform Approach to Valuing Convertible Bonds

“…Ingersoll [14] used this PDE to discuss optimal policies for call and conversion, assuming that CB is the only senior debt in the firm's capital structure. Most of the structural models established previously are considered as extensions of the framework of Merton [24] and Ingersoll [14]; see Batten et al [8] and Bhattacharya [9] for surveys.…”

“…BaroneAdesi et al [6] used a finite element method for solving a two-factor model of CBs under stochastic interest rate and volatility. See Table 3 of Batten et al [8] for recent references on these numerical methods as well as lattice-based and simulation methods.…”

“…A primal target is the CB valuation problem. In recent years, various CBs have been issued with additional conversion provisions, including international CBs [5], CBs with reset clauses [21], reverse CBs [26], mandatory CBs [3] and so on; see Table 2 of Batten et al [8] for detailed features of these variants. However, we only focus on a simple CB with no coupon payments, no call provision and voluntary conversion prior to maturity, because what we are actually aiming at is refining the LCT approach to meet more general claims.…”

Decomposing and valuing convertible bonds: A new method based on exotic options

“…These existing decomposition methods, mainly based on vanilla options, cannot replicate the feature of payoffs of CCBs and PCCBs completely, resulting in significant pricing errors. In the recent literature, simulation methods are usually the favorite choice for pricing path dependent derivatives like convertible bonds, hereafter CBs (Ammann et al, 2008;Batten et al, 2014). Besides, lattice-based numerical methods which include finite-difference method and binomial/trinomial trees are widely used (Anderson and Buffum, 2004;Ayache et al, 2003;Carayannopoulos and Kalimipalli, 2003;Hung and Wang, 2002;Tsiveriotis and Fernandes, 1998).…”