Perpetual American defaultable options in models with random dividends and partial information

Gapeev, Pavel V. ORCID: 0000-0002-1346-2074 and Al Motairi, Hessah (2018) Perpetual American defaultable options in models with random dividends and partial information. Risks, 64 (4). ISSN 2227-9091

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Abstract

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.

Item Type:	Article
Official URL:	https://www.mdpi.com/journal/risks
Additional Information:	© 2018 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	02 Nov 2018 09:15
Last Modified:	17 Nov 2024 02:09
URI:	http://eprints.lse.ac.uk/id/eprint/90535

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