American Parisian options
type: Item
instance of: scholarly article
title: American Parisian options
zbMATH Open document ID: 1126.91025
author: Marc Chesney
author: Laurent Gauthier
published in: Finance and Stochastics
publication date: 2007-05-29T00:00:00Z
full work available at URL: ZORA NL 54042.pdf
review text: The objective of this paper is to develop probabilistic approach for the pricing of American Parisian options. They are described and classified. Put-call parity results are presented. The authors focus purely on currency options. The price of an American Parisian option is decomposed into two components, namely the price of the corresponding European Parisian option and the American premium. The first component is known, and the second one depends on the exercise boundary. The technique of Brownian excursions is used. For perpetual options the exercise boundary is also derived, however, in the case of perpetual American Parisian up-and-out call options it is not a constant. In this case a closed-form solution cannot be obtained. Then the problem is tackled from a different angle, the analogies between American (barrier) and American Parisian barrier options are considered and closed-form expressions are derived or simplifying assumptions are made. A new result concerning the first instant when Brownian motion either hits a positive level or spends a certain time below zero, is obtained.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 62L15
zbMATH DE Number: 5158697
zbMATH Keywords: Parisian option
zbMATH Keywords: American option
zbMATH Keywords: excursion
MaRDI profile type: Publication
OpenAlex ID: W3123310357
cites work: PRICING PARISIAN-STYLE OPTIONS WITH A LATTICE METHOD
cites work: Q4714465
cites work: Brownian Excursions and Parisian Barrier Options
cites work: A combinatorial approach for pricing Parisian options.
cites work: American options: symmetry properties
cites work: Edokko options: a new framework of barrier options
cites work: The valuation of American barrier options using the decomposition technique
cites work: Excursions height- and length-related stopping times, and application to finance
cites work: Optimal stopping for a diffusion with jumps
cites work: Q4226355
DOI: 10.1007/S00780-006-0015-3
description: scientific article; zbMATH DE number 5158697