Pricing VSTOXX Options and Comparing Implied Volatility Methods
Summary
The discussion concerns how to infer implied volatility from options on VSTOXX. It describes an attempt using Black–Scholes with the corresponding VSTOXX futures as the underlying and an assumption about rates and yield, which produced an unsatisfactory gap between call and put smiles. The author reports that Whaley’s model fit better than the other approach they tried, and notes that at-the-money implied volatility can be very high, in line with VIX options.
A cited empirical study compares Whaley, Grunbichler–Longstaff, Carr–Lee, and stochastic-volatility models for VIX options; it is offered as a starting point for applying model comparisons to VSTOXX. The replies also mention model-free implied volatility, which does not require inversion of a particular option pricing model and is used in volatility-index research. The exchange gives no full calibration procedure, numerical comparison details, or consensus conclusion specific to VSTOXX, so its suggestions require independent validation.
Key ideas
- VSTOXX option implied volatility can be estimated using an option pricing model with matching futures as the underlying.
- The question reports that Whaley’s model produced a more satisfactory smile than the alternative it implemented.
- Research comparing models for VIX options can inform, but does not settle, VSTOXX model choice.
- Model-free implied volatility offers an approach that does not depend on a specific option pricing model.
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Full text
# VSTOXX Implied Volatility Calculation # 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%. ## Answer by Matt Wolf (score 6, accepted) https://quant.stackexchange.com/a/8759 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. ## Answer by Rod (score 1) https://quant.stackexchange.com/a/8810 There is another approach to compute Implied Volatility, namely the Model Free Implied Volatility (MFIV). According to this link: > "Unlike the traditional concept of implied volatility, where the implied volatility is estimated numerically from an option pricing model, the model free implied volatility (MFIV) is not dependent on any option pricing model." You can find several papers about MFIV. I suggest you to take a look at SSRN and REPEC, as the MFIV methodology is kind of gaining importance for the computation of volatility indices.
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