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The theory says that the put and call with the same maturity and strike have the same volatility.

I have been resolving the Black Scholes equation after IV using equity and fx market data and I can see that the price for the same maturity with the same strike does not match. Does the difference result from the spread or how is this explainable. How many times do the put/call prices allow for arbitrage in reality?

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  • $\begingroup$ Did you take the bid-ask spread into account? $\endgroup$ – Olaf Dec 11 '15 at 12:31
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I agree to the above answer. The implied volatility should be the same. However if you record the traded option price and derive the implied volatility then these trades should be at the same point in time. For example some rarely traded option could be traded at noon - say a call. Then the put is traded some hours later an you take the last traded price of the underlying. Then your implied vol could differ.

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European Call/Put parity (Call - Put = Discount x (Forward - Strike)), which is a consequence of the nor arbitrage condition, implies that they should be priced using the same implied volatility.

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