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I've been looking at option chains on websites for some popular exchanges (NSE, etc). The exchanges usually provide an implied volatility column in their data, where they're presumably calculating the Black-Scholes or Black76 implied volatility quotes.

The implied volatilities for puts and calls are different despite these being European options (and so violating put call parity). Why is that the case?

As an example, see the IV column from an options snapshot on the NSE: https://www.nseindia.com/option-chain . The IV is not the same for calls and puts of the same expiry and underlying, despite options on the NSE being European style. The IV column shows quite significant differences between calls and puts.

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While put-call parity should theoretically hold, real market conditions can lead to differences in implied volatility due to supply and demand dynamics, market sentiment, and the underlying risks perceived by investors.

For instance, the market dynamics for puts and calls can vary significantly based on investor sentiment. If there’s a higher demand for puts (for hedging purposes, for instance), this can lead to higher implied volatility for puts compared to calls, and vice versa.

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    $\begingroup$ This is wrong. Market dynamics would push them back in line, because if they were varying that significantly there would be arbitrage. $\endgroup$
    – Featherball
    Commented Sep 29 at 14:30
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    $\begingroup$ And why you think that there is no arbitrage? $\endgroup$
    – Sane
    Commented Sep 30 at 7:46

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