Modeling and Pricing VIX Options with Standalone or Joint Models
Summary
The discussion outlines modeling choices for VIX options, including whether to model the VIX directly or build a structural model linking it with the S&P 500 options market. It notes that, although the VIX is calculated from SPX options, VIX derivatives may provide distinct information about volatility dynamics because they offer direct volatility exposure.
For a pricing-focused model, one answer points to a standalone approach that models the VIX without explicitly modeling the S&P 500 market. A model calibrated consistently to both markets is suggested when the goal includes understanding the broader market or estimating risk premia. The discussion also mentions interpolating the VIX implied volatility surface as a practical alternative. These are conceptual recommendations rather than a derivation or empirical comparison; the post supplies no calibration details or evidence establishing which method performs best. It references research on VIX option pricing and volatility dynamics for further study.
Key ideas
- A standalone model can model the VIX directly for pricing VIX options.
- A joint model calibrated to SPX and VIX markets may help represent broader volatility dynamics and risk premia.
- VIX derivatives may convey information distinct from SPX options despite the index’s link to SPX option prices.
- Interpolating the VIX implied volatility surface is another possible practical approach.
- The discussion does not establish a universally best model or provide implementation details.
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# How to value VIX Option? # How to value VIX Option? Could someone tell me a common method for pricing VIX Options please? Do I need to use a Stochastic Vol Model? Or Local Vol Model is suitable as well? Should the model be modelling S&P 500 and then recalculate the VIX Index? Or model the VIX Index directly? Thanks! ## Answer by CharlesM (score 2) https://quant.stackexchange.com/a/9373 I am ignorant to VIX option pricing but I would start with this: The performance of VIX option pricing models: Empirical evidence beyond simulation -- Working paper version ## Answer by Gabriele Pompa (score 1) https://quant.stackexchange.com/a/16168 There's ongoing debate about whether SPX and VIX options contain different valuable information (see Bardgett Gourier Leippold (2013) - Inferring Volatility Dynamics and Risk Premia from the S&P 500 and VIX Markets among recently contributions). I would say this is slightly counterintuitive (VIX index is calculated as a portfolio of SPX vanilla), but at the same time, is the fact that VIX derivatives provide a pure volatility exposure (and traders know it much better than me) that make them conveying a different information, at least concerning volatility dynamics. This said, I would use a consistent model calibrated on both markets. Moreover, in the context of VIX options, there's no Dupire equation (linking VIX option Prices to a VIX implied local volatiliy), but - in some sense parallel - there's an approach called the standalone approach (see Mencìa Sentana (2012) for an update reference), in which one models directly the VIX (without care of the S&P500 market). I would use this If you need a pure pricing machine. But, a structural model as the one I mentioned before is needed to have a perspective of the market as a whole (e.g. estimate risk premia). To conclude, you could off course even simply interpolate the VIX implied surface as is common practice in SPX context. But I don't think this what you meant.
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