PRICING OF PERPETUAL AMERICAN OPTIONS IN A MODEL WITH PARTIAL INFORMATION

Pavel V. Gapeev ()
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Pavel V. Gapeev: Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom

International Journal of Theoretical and Applied Finance (IJTAF), 2012, vol. 15, issue 01, 1-21

Abstract: We study the perpetual American call option pricing problem in a model of a financial market in which the firm issuing a traded asset can regulate the dividend rate by switching it between two constant values. The firm dividend policy is unknown for small investors, who can only observe the prices available from the market. The asset price dynamics are described by a geometric Brownian motion with a random drift rate modeled by a continuous time Markov chain with two states. The optimal exercise time of the option for small investors is found as the first time at which the asset price hits a boundary depending on the current state of the filtering dividend rate estimate. The proof is based on an embedding of the initial problem into a two-dimensional optimal stopping problem and the analysis of the associated parabolic-type free-boundary problem. We also provide closed form estimates for the rational option price and the optimal exercise boundary.

Keywords: Perpetual American option; stochastic dividend rate; discounted two-dimensional optimal stopping problem; stochastic boundary; diffusion process; hidden Markov chain; filtering estimate; innovation process; parabolic-type free-boundary problem; change-of-variable formula with local time on surfaces (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (9)

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DOI: 10.1142/S0219024911006450

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