# VSTOXX Implied Volatility Calculation

What is the industry consensus (if it exists) about implied volatility calculation for options on VSTOXX (OVS)?

I've experimented with the following approach:

• Standard Black-Scholes
• VSTOXX futures as underlying prices for respective option maturities
• Assuming $q=r$

and I wasn't quite happy with the difference between call/put smiles.

I haven't tried Gruenbichler and Longstaff (GL96) yet.

UPD: After implementing GL96 and Whaley, the latter produces much better results.

This is how the smile looks for 30 and 90 days for VSTOXX with Whaley implementation:

UPD2: These numbers are in line with VIX options, where implied volatility of ATM options can reach levels of 120%-130%.

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There is nothing up to interpretation or choice about VSTOXX. It follows a very well defined methodology. What do you mean with "you experimented" with ...? –  Matt Wolf Aug 14 '13 at 14:42
Matt, is this the GL96? –  Eli Aug 14 '13 at 14:56
Forget models, take a look at the methodology, there are a variety of calls and puts involved, no magic there...stoxx.com/download/indices/rulebooks/stoxx_strategy_guide.pdf –  Matt Wolf Aug 14 '13 at 15:05
Matt, I understand how VSTOXX is calculated, the calls and puts involved are the EuroStoxx 50 options. What I need is to calculate the implied volatility for options on VSTOXX: eurexchange.com/exchange-en/products/vol/vol/14550 –  Eli Aug 14 '13 at 15:18
ok, sorry, misunderstood then. Will post something shortly –  Matt Wolf Aug 14 '13 at 15:55

I think you would find the following paper very useful.

It compares different pricing models applied to VIX options. You can use it as starting point to apply to VSTOXX options and see where it gets you.

The Performance of VIX Option Pricing Models: EmpiricalEvidence Beyond Simulation

The following models were tested:

• Whaley (1993)
• Grunbichler and Longstaff (1996)
• Carr and Lee (2007)
• Lin and Chang (2009) (test of 4 different stochastic volatility models

Let me know whether that is what you were after. I myself do not trade vol of vol so not much on that end.

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Yep, that's where I started, I'll try GL96 and then Whaley. Thanks a lot! –  Eli Aug 14 '13 at 16:18
I'll see the results, of course, but it's a great start. I also wonder what is the industry consensus in this respect. Hopefully, we will see more activity/voting in this thread. –  Eli Aug 14 '13 at 19:53
@Eli, the 14% jump in just 1 hour right now in VIX reminds me on your question you asked yesterday. Hopefully this is the kick-off to higher vol markets after this summer lull... –  Matt Wolf Aug 15 '13 at 14:43
Matt, I implemented both models and there are interesting and useful results. If you ever think about trading VSTOXX, there is already implemented and calibrated model. –  Eli Aug 21 '13 at 15:05
@Eli, would you mind sharing some of your findings? Of course only material you do not define as edge, I am simply curious what kind of analysis you have performed and the results you found as far as you feel comfortable commenting on. Would be a rare but highly pleasant treat. –  Matt Wolf Aug 21 '13 at 15:43
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There is another approach to compute Implied Volatility, namely the Model Free Implied Volatility (MFIV).