Pricing VIX Futures under Markov Modulated Regime-Switching Volatility Model: Heston-type model

Abstract

Abstract???? In this paper, we investigate the VIX futures under Markovian modulated Heston-type volatility (MMHV) governed by a two-step Markovian system. The MMHV model formulates not only stochastic volatility process but also volatility process change in states for business cycle. Based on generalized regime-switching Esscher transform, volatility risk premium having an explicit form can be used to link the stochastic volatility to the VIX derivatives via factors of a leverage effect and a double-exponential jump intensity. Under the MMHV model, the VIX futures pricing formula provides the analytical solution by an approximate convexity adjustment method with occupation time of Markov chain. The errors term shows that the approximate closed-form for VIX futures price is accurate value in states of Markov chain. The MMHV model can be used to describe the four typical VIX term structures of Mencia and Sentana (2013) and Lo et al. (2013).