Merton’s model with recovery risk

Albert Cohen and Nick Costanzino

Abstract

In this work, we model the empirically observed recovery risk premium by adding an additional correlated risk driver to Merton’s model for pricing corporate bonds. This risk driver represents the amount of the notional that would be recovered in the event of default. We compute the values of corporate bonds and their related Greeks, and we present the market price of recovery risk. By adding a structural variable, we are also able to decouple equity returns from bond returns, something that is not possible with the classical (one-factor) Merton model. To further address this decoupling, we derive a mapping between the asset–recovery correlation and the correlation of bond and equity returns, as well as a mapping between the asset–recovery correlation and the correlation between the probability of default and the loss given default. In the process of decoupling recovery risk from default risk, we are able to present a model that incorporates an asymmetry between the information set that a manager possesses and the minimal information needed by investors to price bonds and equity. Finally, we employ a numerical algorithm to calibrate to simulated market data with various outstanding notionals as an example of how users can connect this model with bond and equity data.