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Why Short-Dated Equity Options Can Have Higher ATM Implied Volatility

Article Quant Q&A · Author: Will Gu
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Summary

The note examines why an equity option’s annualized at-the-money implied volatility can be higher for a shorter expiry than for a longer one. It distinguishes a downward-sloping volatility term structure from negative forward variance: comparing two implied volatilities alone does not establish that volatility over the later interval is negative. The note says a forward estimate requires assumptions about the relationship between the periods, including independence or a specified correlation.

For single stocks, the suggested explanation is event concentration. Quarterly earnings can contribute a large share of a stock’s volatility, so a short option spanning an announcement may show higher annualized implied volatility than a longer option that also spans just one such event. The note says this pattern is less common for index options. It also states that negative forward variance, calculated using total implied variance across maturities, would imply arbitrage under Black–Scholes dynamics. These are model-dependent observations, not a general arbitrage conclusion from a simple comparison of quoted volatilities.

Key ideas

  • A higher short-expiry annualized implied volatility does not by itself imply negative forward volatility.
  • Forward variance calculations use total variance across maturities and require assumptions about dependence between periods.
  • Earnings announcements can concentrate volatility within a short expiry and elevate its annualized implied volatility.
  • The note distinguishes a downward-sloping volatility term structure from negative forward variance, which it identifies as arbitrage under Black–Scholes dynamics.

Tags

OptionsEquitiesVolatilityDerivatives pricing
Full text
# For equity options, why sometimes ATM vol of shorter expiration is higher than that of longer expiration?


# For equity options, why sometimes ATM vol of shorter expiration is higher than that of longer expiration?












Basically a negative forward vol in the ATM vol term structure. For index options, it's probably rare. But for single name options, I've seen a bunch of examples on Bloomberg. Does this relationship admit some weak form of arbitrage?

Update: I think I have falsely claimed about the forward vol in this situation. Some people might call it "nagative forward vol", but now I don't think it makes much sense (might just be an analogy to interest rate). And as commented in one of the answers, the implied forward vol should be calculated as suggested on Wikipedia, assuming that the two periods are independent of each other. Otherwise, some correlation coefficient is needed in the calculation.

Now I read a bit more on this topic, this kind of phenomenon doesn't admit any arbitrage, but another situation would. If we factor in the time component and calculate the implied variance as $\sigma^2T$, then a "negative forward variance" would admit arbitrage under Black-Scholes dynamics.

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/31475

It doesn't have to imply negative forward vol. for example , 1month 20 Vol and 2 month 19 vol implies (approximately ) that 1 month vol in 1 month time will be 18.

## Answer by Mats Lind (score 0)

https://quant.stackexchange.com/a/31477

A large part of single stock volatility comes just after and around quarterly earnings announcements. An option with short expiry over one announcement thus may price at higher annualized vol than a longer expiry that also encompasses precisely one announcement.

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.