A Simple and Precise Method for Pricing Convertible Bond with Credit Risk

30 Pages Posted: 27 Feb 2014 Last revised: 8 Jan 2019

See all articles by Tim Xiao

Tim Xiao

Risk Models, BMO Capital Markets

Date Written: February 23, 2014

Abstract

This paper presents a new model for valuing hybrid defaultable financial instruments, such as, convertible bonds. In contrast to previous studies, the model relies on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible. As such, the model can back out the market prices of convertible bonds. A prevailing belief in the market is that convertible arbitrage is mainly due to convertible underpricing. Empirically, however, we do not find evidence supporting the underpricing hypothesis. Instead, we find that convertibles have relatively large positive gammas. As a typical convertible arbitrage strategy employs delta-neutral hedging, a large positive gamma can make the portfolio highly profitable, especially for a large movement in the underlying stock price.

Keywords: hybrid financial instrument, convertible bond, convertible underpricing, convertible arbitrage, default time approach (DTA), default probability approach (DPA), jump diffusion

JEL Classification: G21, G12, G24, G32, G33, G18, G28

Suggested Citation

Xiao, Tim, A Simple and Precise Method for Pricing Convertible Bond with Credit Risk (February 23, 2014). Journal of Derivatives and Hedge Funds, November 2013, Volume 19, Issue 4, pp 259–277. Available at SSRN: https://ssrn.com/abstract=2400101

Tim Xiao (Contact Author)

Risk Models, BMO Capital Markets ( email )

Canada

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