ABSTRACT
This paper argues that the reduced-form jump diffusion model may not be
appropriate for credit risk modeling. 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 for a large movement in the underlying
stock price.
Key Words : jump diffusion, convertible bond, convertible
underpricing, convertible arbitrage, default time approach, default
probability approach, asset pricing and credit risk modeling.