Practical Applications from the Experts - May 2009

categories: Product Documentation, general

We have recently implemented a new credit default probability-based convertible bond pricing model. While the old spread-based approach to pricing convertible bonds will continue to be supported, the new default probability approach establishes a direct linkage between credit quality and equity prices. Our extensive library of statistics is available for both these models.

Figure 1 shows a number of Greek Sensitivity statistics on two convertible bonds priced using the credit default probability model. Please note that for deep out-of-the-money convertible bonds such as “Advanced Micro CB 2015” vega is negative. This is expected since increased volatility does not impact “busted” converts and only has an effect on the credit component. “Medtronic CB 2013” convertible bond, although out-of-the-money, is not “busted” and thus has higher equity delta and slightly positive vega.

Figure 1

The new model offers:

• Explicit linkage between credit default probabilities and equity prices at every time step and every node of the equity tree. New model uses either CDS spread or Credit Grade methodology to back out hazard rate term structure to explicitly incorporate credit default probabilities into each step of the calculation.
• More extensive calibration capabilities: the new model has a waterfall structure allowing not only for volatility calibration, recovery rate calibration and credit spread/hazard rate calibration, but also calibration of idiosyncratic hazard rate.
• Ability to incorporate client views as model parameters. Clients are now able to explicitly define their views on implied volatility (either as a number or by setting upper and lower calibration limits), recovery rates and idiosyncratic hazard rates (OAS not explained by economic parameters but nevertheless seen in the market either due to liquidity crises or any other market imbalances)

Download file