Analytical Pricing of American Bond Options in the Heath-Jarrow-Morton Model
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.
Keywords
Cite
@article{arxiv.1212.0781,
title = {Analytical Pricing of American Bond Options in the Heath-Jarrow-Morton Model},
author = {Maria B. Chiarolla and Tiziano De Angelis},
journal= {arXiv preprint arXiv:1212.0781},
year = {2015}
}
Comments
28 pages; we removed the positive part from the discount factor, improved the probabilistic analysis of the value function and provided solutions of the variational inequality in a stronger sense