Causes of Concave Implied Volatility Smiles
Summary
The document discusses why an implied volatility smile can curve downward, with at-the-money volatility above that of out-of-the-money puts and calls. Suggested explanations include negative excess kurtosis, which corresponds to thinner tails than a normal-return benchmark, and mean reversion when the option’s maturity is similar to the underlying’s characteristic reversion time. Such dynamics can limit large price moves relative to a geometric Brownian motion model.
Examples and qualifications are offered rather than a systematic study. Options on VIX futures are cited as a real-market example, with negative curvature reportedly more visible in some longer tenors during 2008 and 2009; the response also warns that Bloomberg’s implied volatility calculations for VIX may be unreliable and that skew can obscure curvature. Another explanation is a market anticipating a binary announcement that could move prices substantially in either direction. The discussion notes that theoretical no-arbitrage conditions may not be practically enforceable when liquidity, spreads, and transaction costs prevent trading.
Key ideas
- Negative excess kurtosis can be associated with a concave implied volatility smile.
- Mean reversion may contribute when option maturity is comparable to the reversion timescale.
- VIX futures options are given as a practical example, with data-quality and skew caveats.
- Anticipation of a binary announcement can create a two-outcome return distribution.
- Market frictions can allow theoretical no-arbitrage violations to persist.
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Full text
# Concave volatility smile # Concave volatility smile Under what circumstances can implied volatility smile be concave (ATM implied volatility higher than OTM put and call)? I know that a slight concavity is not prohibited by no-arbitrage... What are some real-life examples for that? ## Answer by Brian B (score 7, accepted) https://quant.stackexchange.com/a/9059 You can see concavity in mean-reverting underlying assets where the option tenor is comparable to the characteristic reversion time of the asset. For a geometric brownian motion, all underlying prices are possible, so any mean reversion or other limitation on large changes that might occur in reality would ultimately appear as a skinny tail and negative curvature. A good example of real-life negative curvature is options on VIX futures. I include a chart from Bloomberg data below, with the caveats that - Bloomberg is terrible at implying vols for VIX, so one can only see this in their put vols, and - Somehow I typed 3014 in the title Properly implied VIX vols do have negative curvatures as seen here, and were especially pronounced in it during 2008 and 2009 when longer tenors were available. Typically they also have wrong-way skew, which somewhat obscures the negative curvature effects. There are some nice charts, properly done, on page 23 of this paper by Jim Gatheral. ## Answer by Matt Wolf (score 4) https://quant.stackexchange.com/a/9057 Negative excess kurtosis leads to a concave vol smile. By the way, no-arbitrage arguments are of theoretical nature: implied volatilities can exhibit no-arbitrate violations in the theoretical sense for extended periods given that such arbitrate cannot be traded due to other factors, such as liquidity, spreads, transaction related costs...not saying this happens often but it does at times. ## Answer by sashkello (score 4) https://quant.stackexchange.com/a/9325 In addition to the presented answers, I just wanted to mention that such a situation is described in Hull, page 419 (Chapter 19 Volatility Smiles, 19.8: "When a single large jump is anticipated"). This happens when probability distribution of returns is binomial. It can occur in a situation when market is expecting some announcement which will either significantly lift the asset price or drop it.
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