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Estimating ATM Equity Option Volatility with Parametric Smile Fits

Article Quant Q&A · Author: JBerstein
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Summary

The document addresses how to construct an implied volatility smile from US equity options when no traded option has a strike exactly equal to the underlying price. It asks how to estimate at-the-money volatility and connect out-of-the-money put and call observations into a continuous curve. The answer recommends fitting a parametric curve to observed option data, then evaluating that fitted curve at the strike of interest to obtain an ATM value.

The answer also points to the forward price as the key to making call and put implied volatilities consistent where their prices overlap. In equities, estimating the appropriate forward can be difficult because the underlying and option snapshots may be asynchronous, dividends may be uncertain, and borrow costs may be unknown. The discussion is brief: it does not specify a preferred functional form, fitting procedure, or method for handling noisy quotes, so it gives a general construction principle rather than a complete calibration recipe.

Key ideas

  • A fitted parametric volatility curve can provide an implied volatility at a strike without an exact traded quote.
  • Evaluating the fitted curve at the relevant strike gives an estimate of ATM volatility.
  • The forward price is important for aligning call and put volatility curves.
  • Underlying price timing, dividends, and borrow costs can complicate forward estimation in equity options.

Tags

EquitiesOptionsVolatilityDerivatives pricing
Full text
# Non-Trivial ATM Volatility in Vol smile construction from Market data on US Equities


# Non-Trivial ATM Volatility in Vol smile construction from Market data on US Equities












have 2 quick questions please help.

Constructing vol smile (OTM puts & OTM calls) from US equity market data. for Parabolas fit or other methods, the choice/method for ATM vol is non-trivial, since within the market data it is rarely the case that Underlying price == strike price (unlike Fx mkt where we have atm, bf, rr quotations) need help on 2 things.

- In data set underlying price does not equal strike so-> Is there a method to find the correct ATM implied volatility, since the market will certainly not pin the exact ATM strike during the daily computation of the smile.

- What is the common methodology to handle the gap between OTM Calls and OTM puts when connecting the curves to create the smile; continuously and accurately.

Many Thanks!

## Answer by Misha Fomytskyi (score 1)

https://quant.stackexchange.com/a/58416

- The standard way is to fit to a parametric curve and then sample the curve at the strike of interest.

- In order for call and put vols to match you need to have the correct forward. Finding the appropriate forward presents several challenges. For example, in the case of equity options market a) the underlier can be not in sync with the options' snapshot, b) the dividends may not be known, c) the borrow is unknown.

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.