A multi-factor HJM and PCA approach to risk management of VIX futures

Abstract

Purpose Previous studies have shown the VIX futures tend to roll-down the term structure and converge towards the spot as they grow closer to maturity. The purpose of this paper is to propose an approach to improve the volatility index fear factor-level (VIX-level) prediction. Design/methodology/approach First, the authors use a forward-looking technique, the Heath–Jarrow–Morton (HJM) no-arbitrage framework to capture the convergence of the futures contract towards the spot. Second, the authors use principal component analysis (PCA) to reduce dimensionality and save substantial computational time. Third, the authors validate the model with selected VIX futures maturities and test on value-at-risk (VAR) computations. Findings The authors show that the use of multiple factors has a significant impact on the simulated VIX futures distribution, as well as the computations of their VAR (gain in accuracy and computing time). This impact becomes much more compelling when analysing a portfolio of VIX futures of multiple maturities. Research limitations/implications The authors’ approach assumes the variance to be stationary and ignores the volatility smile. Nevertheless, they offer suggestions for future research. Practical implications The VIX-level prediction (the fear factor) is of paramount importance for market makers and participants, as there is no way to replicate the underlying asset of VIX futures. The authors propose a procedure that provides efficiency to both pricing and risk management. Originality/value This paper is the first to apply a forward-looking method by way of a HJM framework combined with PCA to VIX-level prediction in a portfolio context.

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“…For instance, Mencia and Sentana (2013) investigate the pricing and application of VIX derivatives, and Kokholm and Stisen (2015) further the study with the joint pricing of VIX and SPX options under stochastic volatility and jump models. Psychoyios et al (2003) summarize and simulate various different stochastic processes to model the dynamics of market volatility, whereas Belanger and Picard (2018) propose a multiple-factor model to predict the VIX futures distribution curve.…”

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