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Stochastic flows and the forward measure

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Abstract.

Stochastic flows and their Jacobians are used to show why, when the short rate process is described by Gaussian dynamics, (as in the Vasicek or Hull-White models), or square root, affine (Bessel) processes, (as in the Cox-Ingersoll-Ross, or Duffie-Kan models), the bond price is an exponential affine function. Using the forward measure the bond price is obtained by solving a linear ordinary differential equation; Ricatti equations are not required.

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1 (e-mail: relliott@ualberta.ca), , , , , , CA

    Robert J. Elliott

  2. Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia 5005 (e-mail: jvanderh@maths.adelaide.edu.au), , , , , , AU

    John van der Hoek

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  1. Robert J. Elliott
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  2. John van der Hoek
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Mauscript received: February 1999; final version received: October 2000

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Elliott, R., van der Hoek, J. Stochastic flows and the forward measure. Finance Stochast 5, 511–525 (2001). https://doi.org/10.1007/s007800000039

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  • DOI: https://doi.org/10.1007/s007800000039