American options and the free boundary exercise region: a PDE approach
type: Item
instance of: scholarly article
title: American options and the free boundary exercise region: a PDE approach
zbMATH Open document ID: 1178.91179
DOI: 10.4171/IFB/114
author: G. Rapuch
published in: Interfaces and Free Boundaries
publication date: 2005-04-18T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_abstract.php
review text: Summary: American options are classical financial derivative contracts which lead to free boundary problems. The objective of this article is to give some qualitative properties of the exercise region of American options by means of analytic techniques. We prove that the price of an American option is the unique viscosity solution of the obstacle problem. We also prove comparison principles and strict comparison principles. These results enable us to localize the exercise region and to prove the propagation of convexity for American options. As a result, we study the influence of the volatility parameter on the price of American options.
Mathematics Subject Classification ID: 91G10
Mathematics Subject Classification ID: 35R35
zbMATH DE Number: 2157850
zbMATH Keywords: American options
zbMATH Keywords: volatility parameter
zbMATH Keywords: free boundary problem
zbMATH Keywords: obstacle problem
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2157850