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Analytical Pricing of American Bond Options in the Heath-Jarrow-Morton Model


  • Maria B. Chiarolla
  • Tiziano De Angelis


We study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in the Musiela's parametrization of the Heath-Jarrow-Morton (HJM) model for forward interest rates. First we show regularity properties of the price function by probabilistic methods. Then we find an infinite dimensional variational formulation of the pricing problem by approximating the original optimal stopping problem by finite dimensional ones, after a suitable smoothing of the payoff. As expected, the first time the price of the American bond option equals the payoff is shown to be optimal.

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  • Maria B. Chiarolla & Tiziano De Angelis, 2012. "Analytical Pricing of American Bond Options in the Heath-Jarrow-Morton Model," Papers 1212.0781,, revised Mar 2014.
  • Handle: RePEc:arx:papers:1212.0781

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    References listed on IDEAS

    1. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
    2. repec:spr:compst:v:50:y:1999:i:1:p:135-147 is not listed on IDEAS
    3. Camilla Landén & Tomas Björk, 2002. "On the construction of finite dimensional realizations for nonlinear forward rate models," Finance and Stochastics, Springer, vol. 6(3), pages 303-331.
    4. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    5. Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May.
    6. Dariusz Gatarek & Andrzej Świech, 1999. "Optimal stopping in Hilbert spaces and pricing of American options," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 50(1), pages 135-147, August.
    7. Michał Barski & Jerzy Zabczyk, 2012. "Forward rate models with linear volatilities," Finance and Stochastics, Springer, vol. 16(3), pages 537-560, July.
    8. Björk, Tomas & Landen, Camilla, 2000. "On the construction of finite dimensional realizations for nonlinear forward rate models," SSE/EFI Working Paper Series in Economics and Finance 420, Stockholm School of Economics.
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