Title: Is the jump-diffusion model a good solution for credit risk modelling? The case of convertible bonds

Authors: Tim Xiao

Addresses: Risk Models, Capital Markets, BMO, First Canadian Place, 51st Floor, 100 King West, Toronto, ON M5X 1H3, Canada

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.

Keywords: convertible bonds; convertible underpricing; convertible arbitrage; jump diffusion; default time approach; default probability approach; asset pricing; credit risk modelling; hybrid defaultable financial instruments; probability distribution; delta-neutral hedging; stock prices.

DOI: 10.1504/IJFMD.2015.066436

International Journal of Financial Markets and Derivatives, 2015 Vol.4 No.1, pp.1 - 25

Received: 24 Sep 2013
Accepted: 29 Apr 2014
Published online: 19 Dec 2014 *

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