Constructing an Implied Volatility Curve from OTM Options

Summary

The response gives practical guidance for building an implied volatility curve when calls and puts with the same delta show different volatility estimates. It recommends averaging call and put implied volatilities for at-the-money options, while using out-of-the-money options for the wings of the curve. In this approach, puts supply the lower-strike side and calls the higher-strike side; in-the-money options are avoided.

The answer also questions delta as the curve's horizontal coordinate because delta depends on implied volatility, which can create a confounding relationship. It prefers moneyness, such as strike divided by spot, as a coordinate that does not itself include implied volatility. The response reports one practitioner's chosen moneyness band for classifying at-the-money options, but presents it as a personal convention rather than a universal threshold. It offers practitioner guidance, not a comparison of methods or empirical evidence about which curve construction is most accurate.

Key ideas

• Average call and put implied volatilities when constructing the at-the-money point, according to the response.
• Use out-of-the-money options to build the curve's wings.
• Use puts on the lower-strike side and calls on the higher-strike side.
• Avoid in-the-money options for this curve construction approach.
• Moneyness can be preferred to delta because it does not depend on implied volatility.

Tags

# Delta volatility curve construction in practice


# Delta volatility curve construction in practice












I want to construct a volatility curve $\Gamma = \{(\Delta_i, \sigma_i)\}$ but notice that the call and put with the same delta have a different vol (which shouldn't be the case in theory). Is the standard approach to average the call and put vols with the same delta?

## Answer by KaiSqDist (score 2)

https://quant.stackexchange.com/a/80406

Yes it is. However, you should normally do this (average of the call and put IVs) only for ATM options (I myself bound them using moneyness 0.95 < K/S < 1.05).

For options outside these bounds, they are considered as OTM or ITM. You should avoid ITM options and plot the volatility curve using OTM options. For example, the left (right) side of the curve should be OTM put (call) options.

Personally I do not like to use delta as an x-axis, as it produces a confounding effect, I prefer to use moneyness (like K/S), which does not contain the IV.

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