Using Historical VIX Futures Returns for Portfolio Risk

Summary

The document asks how to model VIX futures for portfolio risk management, with emphasis on estimating volatility and correlations rather than pricing. The answer favors empirical historical return distributions because they reflect real-world probabilities, whereas distributions inferred from option pricing models such as Heston are risk-neutral. It also cautions that commonly used stochastic volatility models may not reproduce VIX dynamics well.

The response notes that short-horizon continuous processes can resemble Brownian motion, which may motivate treating VIX similarly to equity index futures. However, it argues that VIX can exhibit substantially larger jumps, making models that ignore this feature potentially inadequate. No software implementation, calibration procedure, sample period, or quantitative comparison is provided. The recommendation is therefore qualitative: historical data is presented as a more relevant starting point for real-world portfolio risk, while jump behavior remains an important modeling concern and the specific approach must be assessed against the intended risk measures.

Key ideas

• Portfolio risk analysis should use real-world return probabilities rather than risk-neutral probabilities alone.
• Historical VIX futures returns are recommended as an empirical basis for risk management.
• The response says standard stochastic volatility models may not capture VIX behavior well.
• VIX futures may have larger jumps than equity index futures, so ignoring jumps can impair risk estimates.

Tags

# Modelling VIX Futures for risk management


# Modelling VIX Futures for risk management












I would like to model VIX futures. The aim is not pricing but risk management. Thus I want to get risk measures like volatility right and be able to accurately calculate correlations when the VIX futures is analyzed in portfolio context.

I am not sure whether the Heston approach that is sometimes used is suitable for this aim. Another approach would be to approximate the VIX futures by the historical returns of the VIX index.

What is the approach most useful in risk management? Do you know any useful software implementation for VIX (e.g. in R)?

## Answer by Brian B (score 1, accepted)

https://quant.stackexchange.com/a/4141

Your idea of using the empirical (historical) distribution makes the most sense for risk management.

For one thing, it ensures you are working with real-world probabilities, whereas obtaining a distribution from an option pricing model (say by fitting Heston to the VIX options) would put you in risk-neutral probability space. For another, the common stochastic vol models all do a poor job of matching VIX dynamics.

Now, any continuous stochastic process looks like a brownian motion in sufficiently short timespans. So the commercial providers are not necessarily crazy to model VIX like equity index futures. However, the dynamics of VIX can be far jumpier than equity index futures, and so I think they are making a mistake by ignoring that aspect.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.