Put–Call Parity and Implied Volatility Differences

Summary

For European options with the same strike and expiry, put–call parity links their prices to the discounted forward price and implies consistent implied volatility when prices and market inputs are aligned. The discussion addresses why observed implied volatilities from puts and calls may nevertheless differ.

The explanation points to asynchronous observations: a thinly traded option may last trade at one time, while its counterpart trades hours later, and the underlying price used in the calculation may also be stale. Such mismatched timestamps can create apparent disagreement without establishing arbitrage. The notes do not quantify how often parity violations occur or give a procedure for measuring executable arbitrage; bid–ask spreads, liquidity, and synchronized quotes remain practical considerations.

Key ideas

• European put–call parity connects call and put prices through the discounted forward and strike.
• Aligned option prices with matching terms imply a common implied volatility under the model.
• Last-trade prices from different times can produce different calculated implied volatilities.
• A stale underlying price can further distort the comparison.
• Observed price differences alone do not establish executable arbitrage.

Tags

# Black Scholes Implied Volatility -> Put call parity


# Black Scholes Implied Volatility -> Put call parity












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?

## Answer by Richi Wa (score 2)

https://quant.stackexchange.com/a/22265

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.

## Answer by Antoine Conze (score 1)

https://quant.stackexchange.com/a/22262

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.