Pricing double barrier options using Laplace transforms
type: Item
instance of: scholarly article
title: Pricing double barrier options using Laplace transforms
zbMATH Open document ID: 0940.91026
author: Antoon Pelsser
published in: Finance and Stochastics
publication date: 2000-05-24T00:00:00Z
review text: Barrier options have become very popular instruments in derivative markets as they are cheaper than standard options but offer a similar kind of protection. It is relatively straightforward to price and hedge ``single barrier'' options. A natural extension to ``single barrier'' options is double barrier options. These options have a barrier above and below the price of the underlying, and the option gets knocked in or out as soon as one of the two barriers is hit. Several papers have already analysed double knock-out and put options and derived expressions for the Laplace transform of the double barrier option price. They invert the Laplace transform numerically to obtain option prices. These papers deal, however, with one type of double barrier option: double barrier knock-out calls and puts. In this paper the author addresses the pricing of double barrier options. To derive the density function of the first-hit times of the barriers the Laplace transform is analytically inverted by contour integration. With these barrier densities pricing formulae for new types of barrier options are derived: knock-out barrier options which pay a rebate when either one of the barriers is hit. Furthermore, more complicated types of barrier options like double knock-in options are discussed.
Mathematics Subject Classification ID: 91G60
Mathematics Subject Classification ID: 44A10
Mathematics Subject Classification ID: 35K05
Mathematics Subject Classification ID: 91G20
zbMATH DE Number: 1452416
zbMATH Keywords: option pricing
zbMATH Keywords: Laplace transform
zbMATH Keywords: contour integration
MaRDI profile type: Publication
full work available at URL: s007800050005
OpenAlex ID: W2023970747
DOI: 10.1007/S007800050005
description: scientific article; zbMATH DE number 1452416