OPTIMAL SELLING TIME OF A STOCK UNDER CAPITAL GAINS TAXES

KÃœHN Christoph (), Budhi Surya and Bjã–rn Ulbricht ()
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KÜHN Christoph: Institut für Mathematik, Johann Wolfgang Goethe-Universität, D-60054 Frankfurt am Main, Germany
Budhi Surya: School of Mathematics and Statistics, Victoria University of Wellington, Wellington 6140, New Zealand
Bjã–rn Ulbricht: DZ Bank AG, D-60325 Frankfurt am Main, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2024, vol. 27, issue 07n08, 1-34

Abstract: We investigate the impact of capital gains taxes on optimal investment decisions in a quite simple model. Namely, we consider a risk-neutral investor in the Black–Scholes model who owns one risky stock and determine the optimal stopping time at which he/she sells the stock to invest the proceeds in the bank account up to the maturity date. At the time the stock is sold, the investor has to realize book profits which triggers tax payments. For a linear tax, we derive a boundary that is continuous and increasing in time and decreasing in the volatility of the stock such that the investor sells the stock at the first time its price is smaller or equal to this boundary. For a variant of the problem with an exponentially distributed time horizon, we determine the boundary explicitly. In addition, we show how the structure of the stopping region changes if there are no tax credits for realized losses in the stock. Some numerical examples are given to exemplify the results.

Keywords: Capital gains taxes; tax-timing option; optimal stopping; free-boundary problem (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0219024925500025

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