The Fractional OU Process: Term Structure Theory and Application

Esben Hoeg and Per Frederiksen
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Esben Hoeg: Aarhus School of Business
Per Frederiksen: Jyske Bank

No 194, Computing in Economics and Finance 2006 from Society for Computational Economics

Abstract: The paper revisits dynamic term structure models (DTSMs) and proposes 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 pricing 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 transform, a no arbitrage price of the bond is recovered by solving a fractional version of the fundamental bond pricing equation. Besides this theoretical contribution, the paper proposes an estimation methodology based on the Kalman filter approach, which is applied to the US term structure of interest rates

Keywords: Fractional bond pricing equation; fractional Brownian motion; fractional Ornstein-Uhlenbeck process; long memory; Kalman Filter (search for similar items in EconPapers)
JEL-codes: C22 C51 E43 (search for similar items in EconPapers)
Date: 2006-07-04
New Economics Papers: this item is included in nep-ets and nep-mac
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Persistent link: https://EconPapers.repec.org/RePEc:sce:scecfa:194

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