Why Matching Call and Put Options Can Have Different Implied Volatility

Summary

For a call and put with the same underlying, strike, and expiration, the note explains why implied volatilities should match in theory. Put-call parity links their prices, and under consistent pricing assumptions that relationship implies the same volatility for both options.

In real markets, reported prices can depart slightly from parity when wide bid-ask spreads or other trading costs make arbitrage impractical. Consequently, separately calculated implied volatilities may differ even for otherwise matching options. The explanation is qualitative: it identifies transaction costs as a possible source of divergence but does not quantify the size of the difference or discuss other pricing inputs and market frictions.

Key ideas

• Put-call parity links prices of calls and puts with matching terms.
• Under consistent theoretical pricing, matching calls and puts should imply the same volatility.
• Wide bid-ask spreads can make parity arbitrage unprofitable.
• Market prices can therefore produce slightly different implied volatilities for matching options.

Tags

# Can a Call and a Put with same strike price and expiration date and underlying asset have different implied volatility?


# Can a Call and a Put with same strike price and expiration date and underlying asset have different implied volatility?












Furthermore, assume that the current price of the underlying asset equals the strike price of the options.

If volatility measures variance without a direction, it doesn't make sense to me that the volatility would be different for a call than for a put with the otherwise same variables.

All this reasoning makes me conclude that the IV should be equal for the call and the put in this case.

## Answer by KaiSqDist (score 5, accepted)

https://quant.stackexchange.com/a/79063

In theory, they shouldn't, but in the real world, it is possible.

In Theory: Call and put options of the same strike and expiry should obey put call parity and thus have the same IV.

In Practice: Call and put prices should obey put call parity due to potential arbitrage opportunities but sometimes there are arbitrage costs such as bid-ask spreads that are unnecessarily wide that make the arbitrage unprofitable. Therefore, they can have (slightly) different IVs.

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.