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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?

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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?

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