Scandinavian Working Papers in Business Administration

Finance Research Group Working Papers,
University of Aarhus, Aarhus School of Business, Department of Business Studies

No F-2008-07: On the Generalized Brownian Motion and its Applications in Finance

Esben Høg (), Per Frederiksen () and Daniel Schiemert ()
Additional contact information
Esben Høg: Department of Business Studies, Aarhus School of Business, Postal: The Aarhus School of Business, Fuglesangs Allé 4, 8210 Aarhus V, Denmark
Per Frederiksen: Equity and Fund Linked Derivatives, Postal: Nordea Markets, Denmark
Daniel Schiemert: Universität Stuttgart;, Postal: Stuttgart, Germany

Abstract: This paper deals with dynamic term structure models (DTSMs) and proposes a new way to handle the limitation of the classical affine models. In particular, the paper expands the exibility of the DTSMs by applying generalized Brownian motions with dependent increments as the governing force of the state variables instead of standard Brownian motions. This is a new direction in pricing non defaultable bonds. By extending the theory developed by Dippon & Schiemert (2006a), the paper developes a bond market with memory, and proves the absence of arbitrage. The framework is readily extendable to other markets or multi factors. As a complement the paper shows an example of how to derive the implied bond pricing parameters using the ordinary Kalman filter.

Keywords: Generalized Brownian motion; Bond market with memory; Fractional bond pricing equation; fractional Ornstein-Uhlenbeck process; long memory; Kalman filter

38 pages, November 1, 2008

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