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Stochastic flows and the forward measure


  • Robert J. Elliott

    () (Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1)

  • John van der Hoek

    () (Department of Applied Mathematics, University of Adelaide, Adelaide, South Australia 5005 Mauscript)


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.

Suggested Citation

  • Robert J. Elliott & John van der Hoek, 2001. "Stochastic flows and the forward measure," Finance and Stochastics, Springer, vol. 5(4), pages 511-525.
  • Handle: RePEc:spr:finsto:v:5:y:2001:i:4:p:511-525
    Note: received: February 1999; final version received: October 2000

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    Cited by:

    1. Hyndman, Cody Blaine, 2007. "Forward-backward SDEs and the CIR model," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1676-1682, November.
    2. Cody Hyndman & Xinghua Zhou, 2014. "Explicit solutions of quadratic FBSDEs arising from quadratic term structure models," Papers 1410.1220,, revised Dec 2014.
    3. Robert Elliott & Rogemar Mamon, 2002. "An interest rate model with a Markovian mean reverting level," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 454-458.
    4. Shen, Yang & Siu, Tak Kuen, 2012. "Asset allocation under stochastic interest rate with regime switching," Economic Modelling, Elsevier, vol. 29(4), pages 1126-1136.
    5. Robert Elliott & Katsumasa Nishide, 2014. "Pricing of discount bonds with a Markov switching regime," Annals of Finance, Springer, vol. 10(3), pages 509-522, August.

    More about this item


    Forward measure; exponential affine; bond pricing;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques


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