Optimal VIX Futures Trading with Mean Reversion and Regime Switching

Summary

The paper formulates optimal trading in VIX futures using a mean-reverting VIX model whose dynamics depend on a regime that switches among a finite set of states. It studies when an investor should enter and leave the market, representing the timing and sequence of participation as optimal double-stopping problems. These decisions lead to coupled systems of variational inequalities.

For numerical solutions, the authors use projected successive over-relaxation with a Crank–Nicolson scheme and illustrate optimal trading boundaries in examples based on a two-state Markov chain. They also examine how transaction costs and the timing of regime changes affect the resulting strategies. The excerpt describes a model and numerical method, but does not give boundary values, empirical tests, or realized trading performance. Its conclusions therefore concern model-based examples; the text does not establish how well the approach works with live VIX futures data or under alternative model assumptions.

Key ideas

• The VIX is modeled as mean reverting with dynamics that vary across switching regimes.
• Trading decisions are framed as optimal entry and exit timing problems.
• The stopping problems produce coupled variational inequalities.
• A projected successive over-relaxation method with a Crank–Nicolson scheme is used numerically.
• Numerical examples examine transaction costs and regime-switching timing, without reporting live trading results.

Tags

# Trading VIX Futures under Mean Reversion with Regime Switching


# Trading VIX Futures under Mean Reversion with Regime Switching









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.

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