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Joint Calibration of Euro Stoxx 50 and VSTOXX Derivatives

Article Quant Q&A · Author: Sinbad The Sailor
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Summary

The document raises a derivatives calibration question by analogy with joint modeling of the S&P 500 and VIX. Since the VIX is derived from S&P 500 options, the author asks whether the Euro Stoxx 50 and VSTOXX should likewise be calibrated together. The European market distinction is that the instruments described for VSTOXX are options on VSTOXX futures, rather than options directly on the volatility index.

No answer or calibration method is included, and the text supplies no model specification, market data, or pricing results. It therefore frames a research problem rather than demonstrating that joint calibration is appropriate. The central issue for further analysis is how the futures-based option instruments relate to the volatility index and to the equity index options used in the analogy. Any practical conclusion would depend on the chosen model and the precise instruments being fitted.

Key ideas

  • The author considers joint calibration of an equity index and its associated volatility index.
  • The proposed analogy is between the S&P 500 with VIX and Euro Stoxx 50 with VSTOXX.
  • The document distinguishes VSTOXX options on futures from options written directly on the index.
  • It poses a modeling question but provides no calibration approach, data, or answer.

Tags

EquitiesOptionsVolatilityDerivatives pricing
Full text
# STOXX50 and VSTOXX joint calibration


# STOXX50 and VSTOXX joint calibration












I am currently researching the joint calibration problem of SPX and VIX. The idea is that: VIX options are derivatives on the VIX, which itself is derived from SPX options and should thus be able to be jointly calibrated.

Looking at European markets there is the STOXX50 and VSTOXX indices both of which are traded. However, on the VSTOXX index only options on futures on the VSTOXX itself are traded.

My question is, using the reasoning behind the SPX/VIX joint calibration, shouldn't the STOXX50 and VSTOXX be jointly calibrated, only that the VSTOXX instruments are options on futures?

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