Efficient Factor Models For Yield Curve Dynamics

This paper derives a class of efficient factor models that bridge a gap between factor models and Heath-Jarrow-Morton models. These efficient factor models provide arbitrage-free dynamics for the yield curve, can be readily extended to fit the current yield curve, and have closed-form formulas for pricing default-free zero-coupon bonds. The short rate is a state variable in these efficient factor models. There are no restrictions imposed on the functional form of the volatility of the short rate except for certain technical conditions to ensure the solvability of the associated stochastic differential equations. The stochastic volatility of the short rate can be one of the state variables. The paper also presents a closed-form solution for default-free discount bond prices in the Malkiel model and provides a new method to derive the Ritchken-Sankarasubramanian model.