  This paper studies the optimal VIX futures trading problems under a
regime-switching model. We consider the VIX as mean reversion dynamics with
dependence on the regime that switches among a finite number of states. For the
trading strategies, we analyze the timings and sequences of the investor's
market participation, which leads to several corresponding coupled system of
variational inequalities. The numerical approach is developed to solve these
optimal double stopping problems by using projected-successive-over-relaxation
(PSOR) method with Crank-Nicolson scheme. We illustrate the optimal boundaries
via numerical examples of two-state Markov chain model. In particular, we
examine the impacts of transaction costs and regime-switching timings on the
VIX futures trading strategies.
