Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion

The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option...

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Detalles Bibliográficos
Autores principales: Sun, Jiao-Jiao, Zhou, Shengwu, Zhang, Yan, Han, Miao, Wang, Fei
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897166/
https://www.ncbi.nlm.nih.gov/pubmed/27433525
http://dx.doi.org/10.1155/2014/746196
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author Sun, Jiao-Jiao
Zhou, Shengwu
Zhang, Yan
Han, Miao
Wang, Fei
author_facet Sun, Jiao-Jiao
Zhou, Shengwu
Zhang, Yan
Han, Miao
Wang, Fei
author_sort Sun, Jiao-Jiao
collection PubMed
description The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed.
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spelling pubmed-48971662016-07-18 Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion Sun, Jiao-Jiao Zhou, Shengwu Zhang, Yan Han, Miao Wang, Fei Int Sch Res Notices Research Article The pricing problem of lookback option with a fixed proportion of transaction costs is investigated when the underlying asset price follows a fractional Brownian motion process. Firstly, using Leland's hedging method a partial differential equation satisfied by the value of the lookback option is derived. Then we obtain its numerical solution by constructing a Crank-Nicolson format. Finally, the effectiveness of the proposed form is verified through a numerical example. Meanwhile, the impact of transaction cost rate and volatility on lookback option value is discussed. Hindawi Publishing Corporation 2014-11-03 /pmc/articles/PMC4897166/ /pubmed/27433525 http://dx.doi.org/10.1155/2014/746196 Text en Copyright © 2014 Jiao-Jiao Sun et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Sun, Jiao-Jiao
Zhou, Shengwu
Zhang, Yan
Han, Miao
Wang, Fei
Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion
title Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion
title_full Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion
title_fullStr Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion
title_full_unstemmed Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion
title_short Lookback Option Pricing with Fixed Proportional Transaction Costs under Fractional Brownian Motion
title_sort lookback option pricing with fixed proportional transaction costs under fractional brownian motion
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4897166/
https://www.ncbi.nlm.nih.gov/pubmed/27433525
http://dx.doi.org/10.1155/2014/746196
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