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

TL;DR

This paper develops an analytical framework for pricing American bond options within the Heath-Jarrow-Morton model, utilizing probabilistic methods and variational formulations to address the infinite-dimensional nature of the problem.

Contribution

It introduces a novel infinite-dimensional variational approach for American bond option pricing in the HJM model, including regularity analysis and finite-dimensional approximations.

Findings

Proved regularity properties of the American bond option price function.

Established an infinite-dimensional variational formulation for the pricing problem.

Demonstrated the optimality of the first hitting time for the payoff.

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.