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Why Implied Volatility Skew Often Flattens at Longer Maturities

Article Quant Q&A · Author: Dom
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Summary

The discussion offers several explanations for why implied-volatility skew or smile may be less pronounced for longer-dated options. One account points to jumps: a jump can have a stronger effect over a short horizon, while its influence may be averaged over a longer horizon. Another explanation focuses on how a given price adjustment for return asymmetry translates into implied volatility. Since option vega is greater for the longer-dated examples, a smaller implied-volatility change can produce a comparable price effect. The response also invokes square-root-of-time scaling to illustrate why the same skew-related price difference can correspond to a smaller volatility increment at a longer maturity.

These are explanatory intuitions rather than a universal law or a model test. The examples use particular option maturities, moneyness levels, and volatility assumptions, and the discussion does not establish that jumps or time scaling alone determine the shape of a market’s term structure. Actual skew depends on market conditions and the underlying return distribution. The note is useful for separating price effects from implied-volatility changes, but it does not give a calibration method or prediction for a specific options market.

Key ideas

  • Short-horizon jumps can have a more concentrated effect on option prices than their influence over longer horizons.
  • A given price adjustment for skew can require a smaller implied-volatility change when option vega is larger.
  • The answer uses square-root-of-time scaling to explain maturity differences in volatility sensitivity.
  • The explanations are intuitive and do not establish a universal cause of flatter long-dated skew.
  • Observed skew can vary with the underlying return distribution and market conditions.

Tags

OptionsVolatilityDerivatives pricing
Full text
# Why is volatility skew/smile for long term options flatter compare to short term options?


# Why is volatility skew/smile for long term options flatter compare to short term options?












Volatility skew/smile for long term options is flatter compared to short term options, could someone help to explain why is that the case? Thanks

## Answer by Magic is in the chain (score 9)

https://quant.stackexchange.com/a/48843

One possible reason could be jumps. Over the longer maturity, there could be more jumps so the jumps average out in a way; whereas over the short term, a jump can make a bigger difference and hence the risk of jump increases demand.

This reasoning is used to justify Stochastic volatility with jumps models in some books.

## Answer by McCabe (score 2)

https://quant.stackexchange.com/a/48854

The skew/smile of long term options is flatter than short term options, the reason for this can be explained in several ways.

The Vega of a shorter-dated option is smaller than a longer-dated option. Vega is the dollar value of a 1% change in implied volatility.

i.e., 30d ATM option, $65 strike, .31 ivol = VEGA .07

30d 25 delta option,31% ivol = VEGA .055

180d ATM option $65 strike 31% ivol =VEGA .18;

180d 25 delta 31% ivol = VEGA.135

Remember, the implied vol smile exists to price in skewness in the underlying assets price returns. Skewness is observed in PRICE CHANGES of the underlying asset, which is then converted to volatility.

So we need to go back to the price in order to bake in expected skewness (observed in the ivol of the OTM options).

Let's presume the skewness of the underlying asset shows a long left-sided tail (larger down moves vs up moves) of roughly 6 cents.

To bake that 6 cents into our OTM option we'd price the 30-day, 25 delta option at ~32% Ivol (1% higher than ATM option)

To bake in that same expected skewness of 6 cents into the 180-day, 25 delta option, the ivol only needs to be increased by .4% or 31.4% Ivol.

Yanyi Yuan's answer is making the same point. The difference in the Square root of time:

i.e., 30 days = SQRT(30/365) = .289; 180 days = SQRT(180/365) = .702 The ratio between the SQRT's of time = .285 / .702 = 40%.

In other words, using the SQRT of time, for the price value of skew to be the same, the implied vol of 180-day option only needs to be increased by .4% for each 1% ivol increase in a 30-day option.

## Answer by Yanyi Yuan (score 1)

https://quant.stackexchange.com/a/48853

The volatilities of short dated options are more sensitive to market changes as compared to those of long dated options. This is implied by square root of time rule. As such, volatility skew are larger for short dated options.

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.