In this paper we study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in the  Heath-Jarrow-Morton (HJM) framework for the forward interest rate. In particular we consider its Musiela's parametrization to guarantee a Markovian setting. Hence we are in an infinite dimensional setting, in which the forward rate curve is described by a SDE in a suitable Hilbert space. In order to find an infinite dimensional variational formulation of the pricing problem , we extend some results on infinite dimensional optimal stopping and variational inequalities recently obtained in 8%DIFDELCMD < ]%%% . The proof goes through three main steps. First we regularize the American bond option's payoff by adopting usual smoothing arguments. Next we approximate the infinite dimensional dynamics by finite dimensional ones to which we associate suitable optimal stopping problems in R^n. Then, by taking the limit as n goes to infinity and by removing the smoothing on the payoff, we obtain an infinite dimensional variational inequality for the price of the American bond option. Moreover ,  the  first time at which the price of the American bond option equals the payoff turns out to be an optimalexercise time .
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 %DIFDELCMD < ]%%% 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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In this paper we
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Musiela's parametrization of the
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framework for the forward interest rate. In particular we consider its Musiela's parametrization to guarantee a Markovian setting. Hence we are in an infinite dimensional setting, in which the forward rate curve is described by a SDE in a suitable Hilbert space. In order to
model for forward interest rates. First we show regularity properties of the price function by probabilistic methods. Then we
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, we extend some results on infinite dimensional optimal stopping and variational inequalities recently obtained in
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. The proof goes through three main steps. First we regularize the American bond option's payoff by adopting usual smoothing arguments. Next we approximate the infinite dimensional dynamics by
by approximating the original optimal stopping problem by
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to which we associate suitable optimal stopping problems in R^n. Then, by taking the limit as n goes to infinity and by removing the smoothing on the payoff, we obtain an infinite dimensional variational inequality for the price of the American bond option. Moreover
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after a suitable smoothing of
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payoff. As expected, the
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at which
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turns out to be an optimalexercise time
is shown to be optimal