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

Pavel V. Gapeev and Hessah Al Motairi
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Pavel V. Gapeev: Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, UK
Hessah Al Motairi: Department of Mathematics, Faculty of Science, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait

Risks, 2018, vol. 6, issue 4, 1-15

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.

Keywords: 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 (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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