The Extended Geske Model and Its Consistency with Reduced Form Models

Abstract

Pioneered by Black and Scholes (1973) and Merton (1974), structural credit models have gained significant attention in recent years. Among the many structural models, the Geske model (1977) maintains the most structure in the original Black-Scholes-Merton model, including endogenously determined default and recovery. It also allows for modeling multiple debts with different seniorities. In this paper, we extend the Geske model to incorporate random interest rates. We derive similar quasi closed form solutions to the ones in Geske. Furthermore, we show that an externally specified default barrier can potentially generate internal inconsistency. Finally, we show that the extended Geske model can be compared with reduced form models in a discretized, binomial framework. This result makes comparison of various models empirically possible. We demonstrate, with a credit derivative example, how different recovery assumptions impact the derivative prices.