OTM Put and Call Volatility Around the Forward

Summary

The document raises a question about constructing a variance-swap replication portfolio from options. It describes an apparent jump in implied volatility when the option wing switches from puts below a strike to calls above it. The quoted explanation is that out-of-the-money options tend to be more liquid, so puts are commonly used at lower strikes and calls at higher strikes, with the forward price defining which options are out of the money.

The author asks whether this convention should create a discontinuity in the implied-volatility curve, whether liquidity is the only reason for choosing those options, and why the forward rather than spot price is the reference. The document does not include the answer to those questions or evidence explaining the observed jump. It is a useful framing of issues in option data selection and variance replication, but it does not establish that a curve break is economically real or describe how to reconcile quotes across the switch.

Key ideas

• Variance-swap replication uses option prices across strikes, making quote selection relevant.
• A common convention uses out-of-the-money puts below the forward and calls above it.
• The document attributes this selection at least partly to the liquidity of out-of-the-money options.
• It asks whether switching option types can explain an apparent implied-volatility discontinuity.
• The prompt leaves the roles of the forward price and other selection reasons unresolved.

Tags

# Implied volatility for puts vs calls


# Implied volatility for puts vs calls












I was trying to create a replication portfolio of options for a Variance Swap and noticed that there is a jump when moving from below strike puts to above strike calls. Something similar to this:

I was curious why would that happen and a quick search brought me to this discussion.

The accepted answer states that:

> In practice you use puts for low strikes and calls for high strikes, since the OTM are more liquid. Low/high is relative to the forward price.

- So if we are using puts for low strikes and calls for high strikes, wouldn't the IV curve be broken at Forward Price?

- Is the reason for using puts for low strikes and calls for high strikes just the liquidity issue? Or are there other reasons for this?

- And finally, why would we use Forward Price, not Spot Price?

Thanks!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.