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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

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

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    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..
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