Simulating American Bond Options in an HJM Framework

Abstract

This paper develops a method called Markov Chain Approximation (MCA) to approximate the value of American bond options in a general multi-factor Heath-JarrowMorton (HJM) framework. Our approach is based on the methodology of Barraquand and Martineau (1995), which was developed for processes which are Markovian in a finite number of state variables. We have extended their methodology to the HJM setting, which in general is only Markovian in an infinite number of state variables. The numerical results obtained from our MCA compare quite closely with closed form or tree solutions. Peter Carr Guang Yang Morgan Stanley Open Link Financial 1585 Broadway, 6th Floor 333 Earle Ovington Blvd, Suite 602 New York, NY 10036 Mitchel Field, NY 11553 (212) 761-7340 (516) 227-6600x209 carrp@ms.com gyang@olf.com Initial Version: August 1, 1996 Current Version: February 26, 1998 We thank Mark Broadie, Zhenyu Duanmu, David Heath, Robert Jarrow, Sergio Kostek, Joseph Langsam, Zack Liu , Dilip Madan, Bill S...