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

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  • Maria B. Chiarolla
  • Tiziano De Angelis
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    Abstract

    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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    File URL: http://arxiv.org/pdf/1212.0781
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1212.0781.

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    Date of creation: Dec 2012
    Date of revision: Mar 2014
    Handle: RePEc:arx:papers:1212.0781

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    1. Heath, David & Jarrow, Robert & Morton, Andrew, 1992. "Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation," Econometrica, Econometric Society, vol. 60(1), pages 77-105, January.
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