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

Listed author(s):
  • Maria B. Chiarolla
  • Tiziano De Angelis
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    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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    Paper provided by in its series Papers with number 1212.0781.

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    Date of creation: Dec 2012
    Date of revision: Mar 2014
    Publication status: Published in Stochastic Processes and their Applications 125 (2015) 678-707
    Handle: RePEc:arx:papers:1212.0781
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    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. 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..
    3. 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.
    4. 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.
    5. repec:spr:compst:v:50:y:1999:i:1:p:135-147 is not listed on IDEAS
    6. 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.
    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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