Why Call and Put Implied Volatilities Can Differ at the Same Strike

Summary

The document examines why an option chain can show different implied volatilities for a call and put at the same strike, despite the relationship between out-of-the-money puts and corresponding in-the-money calls under put-call parity. For American-style options, early exercise means ordinary European put-call parity does not generally hold before expiration, which can contribute to differences in observed prices and implied volatilities.

The answers also note that call-put volatility differences can occur for European options, and that calculation choices or market quotes may be responsible for some apparent gaps. One suggested sanity check is to infer a forward from the option chain using the relationship between call-put mids and strike, then compare the resulting at-the-money volatilities. The reported example found a small relative difference, but it is not presented as a universal result. Mid-quote noise and assumptions about rates, dividends, or repo can affect the comparison, so the document does not identify a single explanation for every chain.

Key ideas

• American early exercise can break European put-call parity before expiration.
• Call-put implied-volatility differences can also appear in European options.
• Inconsistent assumptions about rates, dividends, or repo may distort implied-volatility comparisons.
• Inferring a forward from call-put mid quotes is one possible diagnostic, though quote noise remains.

Tags

# Why is IV different between put and call of same strike


# Why is IV different between put and call of same strike












In his book 'Dynamic Hedging' Nassim Taleb says that the volatility of an OTM put should be exactly equal to that of a corresponding in the money call of same strike.

But in option chains, the calls always have a slightly higher IV than the corresponding put.

Is this because I am looking at American option chains and not European?

## Answer by Eli (score 6, accepted)

https://quant.stackexchange.com/a/17484

Since American style options allow early exercise, put-call parity will not hold for American options (unless they are held to expiration).

In practice, there is also a difference between calls and puts for European options as well. The full description is here: What causes the call and put volatility surface to differ?

## Answer by Hilbert (score 0)

https://quant.stackexchange.com/a/85463

The explanation can be less complicated as sometimes I stumbled upon a dataset where the IV and the greeks were computed from Black-Scholes being used in a very weird way (like making assumptions about the risk-free rate, div and repo rate).

When computed with the implied forward (by performing a linear regression on the entire option chain as strike the explanatory variable and the mid_call-mid_put as the variable to explain) the ATM vol difference between calls and puts was less than 1% in relative which might be attributed to the call-put parity computation being performed by using mid quotes.

I don't say that this is the reason, but this should be the first sanity check.

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.