Timing in the Presence of Directional Predictability: Optimal Stopping of Skew Brownian Motion

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Publication Details

List of Authors: Luis H. R. Alvarez E., Paavo Salminen
Publisher: ArXiv.org
Publication year: 2016


We investigate a class of optimal stopping problems arising in, for
example, studies considering the timing of an irreversible investment when
the underlying follows a skew Brownian motion. Our results indicate that the
local directional predictability modeled by the presence of a skew point for
the underlying has a nontrivial and somewhat surprising impact on the timing
incentives of the decision maker. We prove that waiting is always optimal at
the skew point for a large class of exercise payoffs. An interesting consequence
of this finding, which is in sharp contrast with studies relying on ordinary
Brownian motion, is that the exercise region for the problem can become
unconnected even when the payoff is linear. We also establish that higher
skewness increases the incentives to wait and postpones the optimal timing of
an investment opportunity. Our general results are explicitly illustrated for a
piecewise linear payoff.

Last updated on 2020-17-01 at 04:14