Convertible Bond Prices and Inherent Biases

Abstract

O ur objective is to examine the pricing behavior of corporate convertible bonds that are currently traded in the U.S. secondary convertible bond market. No study to date has used recent data from the U.S. convertible bond market, so our work contributes significantly to an understanding of this market.The model follows the Duffie and Singleton [1999] credit risk model. This approach lets us calibrate default probabilities in the model to the market prices of both risky debt and equity.Our results indicate that convertible bonds with relatively low conversion value are often underpriced to the extent that their prices regularly violate pricing bounds implied by the presence of the conversion option. For such bonds, we find that the boundary condition associated with the bond's straight debt value is often violated, and negative option prices are implied. The differences between actual and model prices for bonds with low conversion value are not the result of biases inherent in the pricing model used but are instead attributable to a systematic underpricing of these bonds in the marketplace.This finding should be of importance to corporate debt issuers and investors alike, in the wake of the tremendous growth in the convertible bond market. 1 I. LITERATURE REVIEWThe convertible bond is a hybrid security that combines straight bond characteristics with a conversion feature. This feature allows the owner to exchange the convertible bond for another security of different characteristics, usually the issuing firm's common stock. Therefore, while it retains most of the characteristics of straight debt, the convertible bond also offers an upside potential associated with the underlying common stock. Given its hybrid nature, valuation of a convertible bond requires a model that captures both its exposure to credit risk and the upside potential from its equity-like behavior.Credit risk models are generally classified in two categories: structural models and reducedform models. 2 Structural models assume the value of a firm is continuous over time and, given the dynamics of firm value through time and appropriate terminal and boundary conditions, derive the value of the firm's debt. Merton [1974] developed one of the first models, which assumes that default is allowed only at the maturity of the debt. Subsequent structural models relax some of the unrealistic assumptions of the Merton [1974] model. 3 Default can instead occur any time during the life of the bond, and default is triggered when the value of the firm reaches a certain threshold level. Problems arising from unobservable variables and complex capital structure still limit the practical application of such models.

A simple and precise method for pricing convertible bond with credit risk

“…Underpricing is referred to as the model price minus the market price. we do not find support for presence of a systematic underpricing as indicated in previous studies (see Carayannopoulos and Kalimipalli (2003), Ammann et al (2003), and so on). If there is no underpricing, how has the arbitrage strategy been successful in the past?…”

Is the Jump-Diffusion Model a Good Solution for Credit Risk Modeling? The Case of Convertible Bonds

“…Empirically, we do not find support for presence of a systematic underpricing as indicated in previous studies (see Carayannopoulos and Kalimipalli (2003), Ammann, Kind and Wilde (2003), etc.). If there is no underpricing, how has the arbitrage strategy been successful in the past?…”

What drives the performance of convertible-bond funds?

“…** 5% significance. *** 1% significance.17 Several studies, such asCarayannopoulos and Kalimipalli (2003),Ammann et al (2003Ammann et al ( , 2008 document that market prices for convertible bonds deviate substantially from ''fair" values as determined by conventional no-arbitrage models.…”