Analytical pricing of American Put options on a Zero Coupon Bond in the Heath-Jarrow-Morton model

被引：3
|
作者：
Chiarolla, Maria B. [1 ]
De Angelis, Tiziano [2 ]
机构：
[1] Univ Roma La Sapienza, Dipartimento Metodi & Modelli Econ Terr & Finanza, I-00161 Rome, Italy
[2] Univ Manchester, Sch Math, Manchester M13 9PL, Lancs, England
来源：
STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2015年 / 125卷 / 02期
基金：
英国工程与自然科学研究理事会;
关键词：
American Put options on a Bond; HJM model; Forward interest rates; Musiela's parametrization; Optimal stopping; Infinite-dimensional stochastic analysis; TERM STRUCTURE; VARIATIONAL-INEQUALITIES; REALIZATIONS; EXISTENCE; RATES;
D O I：
10.1016/j.spa.2014.09.021
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
We study the optimal stopping problem of pricing an American Put option on a Zero Coupon Bond (ZCB) in 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. (C) 2014 Elsevier B.V. All rights reserved.
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页码：678 / 707
页数：30
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