A Two-Mean Reverting-Factor Model of the Term Structure of Interest Rates

Abstract

This paper presents a two--factor model of the term structure of interest rates. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long--term interest rate and the spread (difference between the long--term rate and the short--term (instantaneous) riskless rate). Assuming that both factors follow a joint Ornstein--Uhlenbeck process, a general bond pricing equation is derived. We obtain a closed--form expression for bond prices and examine its implications for the term structure of interest rates. We also derive a closed--form solution for interest rate derivatives prices. This expression is applied to price European options on discount bonds and more complex types of options. Finally, empirical evidence of the model's performance is presented.