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Stochastic flows and the forward measure

Author

Listed:
  • 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)

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.

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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    Citations

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    Cited by:

    1. Zhao, Yixing & Mamon, Rogemar & Gao, Huan, 2018. "A two-decrement model for the valuation and risk measurement of a guaranteed annuity option," Econometrics and Statistics, Elsevier, vol. 8(C), pages 231-249.
    2. Robert J. Elliott & Katsumasa Nishide, 2013. "Pricing of Discount Bonds with a Markov Switching Regime　," KIER Working Papers 859, Kyoto University, Institute of Economic Research.
    3. Shen, Yang & Siu, Tak Kuen, 2012. "Asset allocation under stochastic interest rate with regime switching," Economic Modelling, Elsevier, vol. 29(4), pages 1126-1136.
    4. Marianito R. Rodrigo & Rogemar S. Mamon, 2014. "An alternative approach to the calibration of the Vasicek and CIR interest rate models via generating functions," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1961-1970, November.
    5. Hyndman, Cody Blaine, 2007. "Forward-backward SDEs and the CIR model," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1676-1682, November.
    6. 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.
    7. Cody Hyndman & Xinghua Zhou, 2014. "Explicit solutions of quadratic FBSDEs arising from quadratic term structure models," Papers 1410.1220, arXiv.org, revised Dec 2014.
    8. 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

    Keywords

    Forward measure; exponential affine; bond pricing;
    All these keywords.

    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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