The Fractional Ornstein-Uhlenbeck Process: Term Structure Theory and Application

Abstract

The paper revisits dynamic term structure models (DTSMs) and pro-poses a new way in dealing with the limitation of the classical affine models. In particular, this paper expands the flexibility of the DTSMs by applying a fractional Brownian motion as the governing force of the state variable instead of the standard Brownian motion. This is a new direction in pric-ing non defaultable bonds with offspring in the arbitrage free pricing of weather derivatives based on fractional Brownian motions. By applying fractional Ito ̂ calculus and a fractional version of the Girsanov trans-form, a no arbitrage price of the bond is recovered by solving a fractional version of the fundamental bond pricing equation. Besides this theoreti-cal contribution, the paper proposes an estimation methodology based on the Kalman filter approach, which is applied to the US term structure of interest rates.