Abstract
This paper argues that the reduced–form jump diffusion model may not be appropriate for credit risk modelling. To correctly value hybrid defaultable financial instruments, e.g., convertible bonds, we present a new framework that 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 or a large movement in the underlying stock price.
Highlights
A company can raise capital in financial markets either by issuing equities, bonds, or hybrids
In contrast to the above mentioned literature, we present a model that is based on the probability distribution of a default jump rather than the default jump itself, as the default jump is usually inaccessible (see Duffie and Huang (1996), Jarrow and Protter (2004), etc)
We study the sensitivities of convertible bonds and find that convertible bonds have relatively large positive gammas, implying that convertible arbitrage can make a profit on a large upside or downside movement in the underlying stock price
Summary
A company can raise capital in financial markets either by issuing equities, bonds, or hybrids (such as convertible bonds). As a matter of fact, we will prove that the expected return of a defaultable asset under a risk-neutral measure grows at a risky rate rather than the risk-free rate This conclusion is very important for risky valuation. We will show in the following derivation that the expected return of a defaultable asset under a risk-neutral measure is equal to a risky rate instead of the risk-free rate. The market bond model says that the value of a risky bond is obtained by discounting the promised payoff using the risk-free interest rate plus the credit spread. The risky rate reflects the compensation investors receive for bearing credit risk
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: International Journal of Financial Markets and Derivatives
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.