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

Philippe Bélanger (Finance, Assurance et Immobilier, Laval University, Québec, Canada)
Marc-André Picard (FINCAD, Surrey, Canada)

Journal of Risk Finance

ISSN: 1526-5943

Article publication date: 31 October 2018

Issue publication date: 27 November 2018



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.


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.


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.


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.



Thanks to Prof Van Son Lai for his mentoring. The authors would like to thank the anonymous referee and Dr Bonnie Buchanan for their very constructive and insightful comments and suggestions, which have greatly enhanced the quality of the paper.

Disclaimer: The views and opinions expressed in this publication are those of the authors alone and do not necessarily represent the views of the FinancialCAD corporation or any of its affiliates.


Bélanger, P. and Picard, M.-A. (2018), "A multi-factor HJM and PCA approach to risk management of VIX futures", Journal of Risk Finance, Vol. 19 No. 5, pp. 524-547.



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