Trading VIX futures under mean reversion with regime switching

Abstract

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 twostate Markov chain model. In particular, we examine the impacts of transaction costs and regime-switching timings on the VIX futures trading strategies.

Integral equation characterization of the Feynman–Kac formula for a regime-switching diffusion

“…[10] and references therein). This expectation can be approximated by numerically solving the coupled PDE in (1.1) by finite-difference methods ( [3], [5], [8]), by trinomial tree methods ( [9]), or by Monte Carlo simulation ( [7]). In this paper, we propose an analytical representation of v in (1.2) as the fixed point of an integral equation where we exploit the contraction theorem on Banach spaces.…”