Perpetual American Defaultable Options in Models with Random Dividends and Partial Information

We present closed-form solutions to the perpetual American dividend-paying put and call option pricing problems in two extensions of the Black⁻Merton⁻Scholes model with random dividends under full and partial information. We assume that the dividend rate of the underlying asset p...

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Main Authors:	Pavel V. Gapeev, Hessah Al Motairi
Format:	Article
Language:	English
Published:	MDPI AG 2018-11-01
Series:	Risks
Subjects:	perpetual American options random dividends optimal stopping problem Brownian motion hidden Markov chain filtering estimate innovation process free-boundary problem a change-of-variable formula with local time on surfaces
Online Access:	https://www.mdpi.com/2227-9091/6/4/127

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spelling	doaj-188e04337efa4ed8be81515a96df5e382020-11-25T00:37:13ZengMDPI AGRisks2227-90912018-11-016412710.3390/risks6040127risks6040127Perpetual American Defaultable Options in Models with Random Dividends and Partial InformationPavel V. Gapeev0Hessah Al Motairi1Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UKDepartment of Mathematics, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, KuwaitWe present closed-form solutions to the perpetual American dividend-paying put and call option pricing problems in two extensions of the Black⁻Merton⁻Scholes model with random dividends under full and partial information. We assume that the dividend rate of the underlying asset price changes its value at a certain random time which has an exponential distribution and is independent of the standard Brownian motion driving the price of the underlying risky asset. In the full information version of the model, it is assumed that this time is observable to the option holder, while in the partial information version of the model, it is assumed that this time is unobservable to the option holder. The optimal exercise times are shown to be the first times at which the underlying risky asset price process hits certain constant levels. The proof is based on the solutions of the associated free-boundary problems and the applications of the change-of-variable formula.https://www.mdpi.com/2227-9091/6/4/127perpetual American optionsrandom dividendsoptimal stopping problemBrownian motionhidden Markov chainfiltering estimateinnovation processfree-boundary problema change-of-variable formula with local time on surfaces
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Pavel V. Gapeev Hessah Al Motairi
spellingShingle	Pavel V. Gapeev Hessah Al Motairi Perpetual American Defaultable Options in Models with Random Dividends and Partial Information Risks perpetual American options random dividends optimal stopping problem Brownian motion hidden Markov chain filtering estimate innovation process free-boundary problem a change-of-variable formula with local time on surfaces
author_facet	Pavel V. Gapeev Hessah Al Motairi
author_sort	Pavel V. Gapeev
title	Perpetual American Defaultable Options in Models with Random Dividends and Partial Information
title_short	Perpetual American Defaultable Options in Models with Random Dividends and Partial Information
title_full	Perpetual American Defaultable Options in Models with Random Dividends and Partial Information
title_fullStr	Perpetual American Defaultable Options in Models with Random Dividends and Partial Information
title_full_unstemmed	Perpetual American Defaultable Options in Models with Random Dividends and Partial Information
title_sort	perpetual american defaultable options in models with random dividends and partial information
publisher	MDPI AG
series	Risks
issn	2227-9091
publishDate	2018-11-01
description	We present closed-form solutions to the perpetual American dividend-paying put and call option pricing problems in two extensions of the Black⁻Merton⁻Scholes model with random dividends under full and partial information. We assume that the dividend rate of the underlying asset price changes its value at a certain random time which has an exponential distribution and is independent of the standard Brownian motion driving the price of the underlying risky asset. In the full information version of the model, it is assumed that this time is observable to the option holder, while in the partial information version of the model, it is assumed that this time is unobservable to the option holder. The optimal exercise times are shown to be the first times at which the underlying risky asset price process hits certain constant levels. The proof is based on the solutions of the associated free-boundary problems and the applications of the change-of-variable formula.
topic	perpetual American options random dividends optimal stopping problem Brownian motion hidden Markov chain filtering estimate innovation process free-boundary problem a change-of-variable formula with local time on surfaces
url	https://www.mdpi.com/2227-9091/6/4/127
work_keys_str_mv	AT pavelvgapeev perpetualamericandefaultableoptionsinmodelswithrandomdividendsandpartialinformation AT hessahalmotairi perpetualamericandefaultableoptionsinmodelswithrandomdividendsandpartialinformation
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Perpetual American Defaultable Options in Models with Random Dividends and Partial Information

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