A Stochastic Model for Default-Free Bond Prices and Continuously Compounding Yield-to-Maturity

Abstract

The following article examines a stochastic, log-normal model for the continuously compounding yield-to-maturity and a corresponding price model for default-free zero coupon bonds. This article sets conditions for the validity of the model and goes on to show that this model is a special case of the Heath, Jarrow and Morton (HJM) model for forward interest rates, and it examines the conditions for the equivalence. We show that given these conditions, the HJM model and the continuously compounding yield-to-maturity model have the same market price of risk and thus, must satisfy identical conditions for the existence and uniqueness of a risk-neutral measure.