Skip to content
All library documents

Choosing Time to Expiry in Black Pricing for VIX Futures Options

Article Quant Q&A · Author: deblue
Read the original

Summary

The discussion clarifies which expiry to use when applying a Black-style model to an option on a VIX future. It says to use the option’s exchange-published expiration date, measured from the valuation date, rather than the maturity of the underlying futures contract. The response does not address the question’s alternative proposal of simulating a futures curve with correlated geometric Brownian motions.

Time to expiry must be expressed as a fraction of a year. The answer notes two conventions: counting calendar days against a 365-day year or trading days against a 250-day year. It leaves the choice between these conventions open, so practitioners should use a convention consistent with their model inputs and market practice. The document offers no pricing example, calibration guidance, or analysis specific to VIX futures; its main takeaway is the distinction between option expiry and futures maturity.

Key ideas

  • Use the option’s listed exchange expiration as the model’s expiry date.
  • Measure time from the valuation date to that expiration.
  • Convert remaining days into a year fraction before using the model.
  • Calendar-day and trading-day annualization conventions are both mentioned, with no definitive preference.

Tags

OptionsFuturesDerivatives pricing
Full text
# Black76: Pricing options on futures


# Black76: Pricing options on futures












I am trying to roughly approximate (not really price) options on VIX futures whereby the VIX future is estimated using their bounds. If the option is approximated using the Black model, how do you determine the expiry T in the F(t,T) curve to use in the formula?

Alternatively, can you price the option by simulating the futures curve using a multivariate GBM? Any references?

## Answer by Con Fluentsy (score 2)

https://quant.stackexchange.com/a/60003

The expiry to T,t in any option model is simply the published expiry date on the exchange, at the close of trade. The time till expiry is simply the number of outstanding days till this occurrence, dates time is converted to a percentage of a year no of days / either 250 trading days OR 365 calendar days, that is another discussion, outside of this scope, whether trading days or calendar days. Both are used freely.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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