Reading the Volatility Smile: What Strike Skew Tells You About Crash Risk

Summary. The implied volatility smile describes how option prices vary across strikes, and its shape encodes the market's risk-neutral distribution for the underlying. For equity indices the smile has been steeply downward sloping since the 1987 crash. This article explains what the slope means in distributional terms, recovers the implied density from a stylized smile, reviews the explanations for index skew, defines the standard skew measures, and discusses what changes in skew do and do not tell you.

1. From prices to a distribution

Under the Black-Scholes model all strikes share one implied volatility. In practice they do not, and the pattern of implied volatility across strikes is the smile. Breeden and Litzenberger showed that the risk-neutral density of the underlying at expiry is the second derivative of call prices with respect to the strike [1]:

The smile is therefore not a separate signal from option prices; it is a compact way of describing the distribution they imply. A smile that rises toward low strikes means the market assigns more probability to large declines than a lognormal distribution would.

2. The shape of the index smile

Before October 1987, S&P 500 index options showed little skew. Since then, out-of-the-money puts have traded at persistently higher implied volatility than at-the-money options, which in turn trade above out-of-the-money calls [2, 3]. Practitioners call this downward-sloping shape a smirk or skew. Figure 1 shows two stylized one-month smiles generated with Gatheral's SVI parameterization [4], one for calm conditions and one for stressed conditions.

Applying the Breeden-Litzenberger formula to the calm smile gives the density in Figure 2. Compared with a lognormal at the same at-the-money volatility, the implied density has a thicker left tail and a thinner right tail. The skew is the price of that extra left-tail probability.

3. Why index skew exists

• Crash risk. Bates shows that after 1987, S&P 500 futures option prices imply substantial risk of large downward jumps [3].
• Volatility rises when prices fall. Index volatility tends to increase in declines, the leverage effect first documented by Black [5]. A distribution in which declines come with higher volatility is left-skewed, which steepens the smile.
• Demand pressure. Bollen and Whaley show that net buying pressure on index puts moves their implied volatilities [6], and Gârleanu, Pedersen and Poteshman show theoretically and empirically that end-user demand for options that dealers cannot hedge perfectly raises their prices, with the effect concentrated in index puts [7].

The second channel is easy to see in daily data (Figure 3). From October 2016 to October 2026, daily S&P 500 returns and daily changes in the VIX had a correlation of −0.79 [8, 9]. A simple regression gives a slope of about −1.4 VIX points per 1% index move. The VIX rose by 1.03 points on the average down day and fell by 0.85 points on the average up day, and the two moved in opposite directions on 78% of days. A distribution whose volatility rises as it falls has a heavier left tail, which is what the smile prices.

4. Measuring skew

The most common practitioner measure is the 25-delta risk reversal, the implied volatility of the put with delta −0.25 minus that of the call with delta +0.25:

For the calm stylized smile above, the 25-delta put sits about 3.3% below spot and the 25-delta call about 2.2% above, and the risk reversal is about 6.8 volatility points. For the stressed smile the strikes are wider (about 5.3% below and 4.4% above) and the risk reversal is about 8.4 points. Other measures include the slope of implied volatility per unit of log-moneyness, the ratio of put to at-the-money volatility, and the Cboe SKEW Index, which measures the risk-neutral skewness of 30-day S&P 500 returns from out-of-the-money option prices [10].

Two cautions apply when comparing skew over time. First, measures defined by delta move their strikes with the level of volatility, so a higher risk reversal in a high-volatility regime partly reflects strikes further from spot. Second, skew in volatility points tends to rise with the volatility level; normalizing by at-the-money volatility makes periods more comparable.

5. What changes in skew indicate

• Steepening with stable spot. Rising put volatility relative to at-the-money volatility indicates more demand for downside protection or a higher priced probability of a decline. For individual stocks, Xing, Zhang and Zhao find that firms with the steepest smirks subsequently underperform, consistent with informed traders using out-of-the-money puts [11].
• Flattening. A flatter skew can reflect reduced hedging demand or increased call demand. Open interest helps separate the two: rising call open interest with a flatter skew points to call buying, while flat open interest points to less hedging.
• Event premiums. Options spanning major political or macro events carry extra premium, often concentrated in the wings [12].

These are associations, not timing signals. Skew can stay steep for long periods without a decline, because insurance demand is persistent.

6. Skew and dealer positioning

Skew also affects the dealer positioning measures used elsewhere on this blog. Gamma, vanna and charm depend on each strike's implied volatility; computing them with a flat volatility understates the gamma of out-of-the-money puts relative to calls when the smile is steep. Positioning models should use strike-specific implied volatility. And because dealers are typically short index puts, a steepening skew raises the value of the inventory they are short, which interacts with the vanna flows discussed in vanna walls versus gamma walls.

7. Practical reading

1. Track a delta-based risk reversal and a moneyness-based slope together, normalized by at-the-money volatility.
2. Compare the current smile with its own recent history for the same tenor rather than with a fixed threshold.
3. Check open interest changes to separate hedging demand from call demand.
4. Use strike-specific implied volatility when computing exposures.

DataFirst's surface view shows the full smile for each expiry so changes in shape are visible alongside the positioning map.

For educational and informational purposes only. Not financial advice. Options trading involves substantial risk of loss. Smiles in the figures are stylized SVI curves, not market data.

References

1. Breeden, D. T., & Litzenberger, R. H. (1978). Prices of state-contingent claims implicit in option prices. Journal of Business, 51(4), 621–651. doi.org/10.1086/296025
2. Rubinstein, M. (1994). Implied binomial trees. Journal of Finance, 49(3), 771–818. doi.org/10.1111/j.1540-6261.1994.tb00079.x
3. Bates, D. S. (2000). Post-'87 crash fears in the S&P 500 futures option market. Journal of Econometrics, 94(1–2), 181–238. doi.org/10.1016/S0304-4076(99)00021-4
4. Gatheral, J. (2006). The Volatility Surface: A Practitioner's Guide. Wiley.
5. Black, F. (1976). Studies of stock price volatility changes. Proceedings of the 1976 Meetings of the American Statistical Association, Business and Economic Statistics Section, 177–181.
6. Bollen, N. P. B., & Whaley, R. E. (2004). Does net buying pressure affect the shape of implied volatility functions? Journal of Finance, 59(2), 711–753. doi.org/10.1111/j.1540-6261.2004.00647.x
7. Gârleanu, N., Pedersen, L. H., & Poteshman, A. M. (2009). Demand-based option pricing. Review of Financial Studies, 22(10), 4259–4299. doi.org/10.1093/rfs/hhp005
8. S&P Dow Jones Indices LLC. S&P 500 [SP500]. Retrieved from FRED, Federal Reserve Bank of St. Louis, 9 October 2026. fred.stlouisfed.org/series/SP500
9. Cboe Global Markets. Cboe Volatility Index: VIX [VIXCLS]. Retrieved from FRED, Federal Reserve Bank of St. Louis, 9 October 2026. fred.stlouisfed.org/series/VIXCLS
10. Cboe Global Markets. Cboe SKEW Index. Index dashboard and methodology. www.cboe.com/us/indices/dashboard/skew/
11. Xing, Y., Zhang, X., & Zhao, R. (2010). What does the individual option volatility smirk tell us about future equity returns? Journal of Financial and Quantitative Analysis, 45(3), 641–662. doi.org/10.1017/S0022109010000220
12. Kelly, B., Pástor, Ľ., & Veronesi, P. (2016). The price of political uncertainty: Theory and evidence from the option market. Journal of Finance, 71(5), 2417–2480. doi.org/10.1111/jofi.12406