Some applications of occupation times of Brownian motion with drift in mathematical finance
type: Item
instance of: scholarly article
title: Some applications of occupation times of Brownian motion with drift in mathematical finance
zbMATH Open document ID: 0933.91017
DOI: 10.1155/S1173912699000048
author: Andreas Pechtl
published in: Journal of Applied Mathematics and Decision Sciences
publication date: 1999-09-22T00:00:00Z
full work available at URL: https://eudml.org/doc/120176
review text: Summary: In the last few years new types of path-dependent options called corridor options or range options have become well-known derivative instruments in European options markets. Since the payout profiles of those options are based on occupation times of the underlying security the purpose of this paper is to provide closed form pricing formulae of Black-Scholes type for some significant representatives. Alternatively we demonstrate in this paper a relatively simple derivation of the Black-Scholes price for a single corridor option -- based on a static portfolio representation -- which does not make use of the distribution of occupation times (of Brownian motion). However, knowledge of occupation times' distributions is a more powerful tool.
Mathematics Subject Classification ID: 91B28
zbMATH DE Number: 1340877
zbMATH Keywords: Brownian motion drift
zbMATH Keywords: Black-Scholes model
zbMATH Keywords: corridor options
zbMATH Keywords: European options markets
zbMATH Keywords: occupation times
MaRDI profile type: Publication
OpenAlex ID: W2115539870
description: scientific article; zbMATH DE number 1340877