Put-Call Implied Volatility at the Forward At-the-Money Strike

Summary

The document explains when European calls and puts with the same strike and maturity should have matching implied volatilities. Under put-call parity, their implied volatilities coincide at the at-the-money forward strike when the other pricing inputs are consistent. At-the-money by spot price is a different point unless the forward price equals spot.

The distinction helps explain why observed call and put implied volatilities can differ for stocks with substantial dividends or borrowing costs, which can move the forward away from spot. The answer also cautions that American options do not satisfy European put-call parity in the same way; parity instead supplies bounds. The discussion is a concise conceptual explanation, with no data analysis or numerical examples establishing the size of these effects in particular stocks.

Key ideas

• European calls and puts with matching terms have equal implied volatility at the at-the-money forward strike under put-call parity.
• At-the-money spot and at-the-money forward are different when the forward price differs from spot.
• Dividends and stock borrowing costs can shift the forward price and explain apparent call-put volatility differences at spot ATM.
• For American exercise, put-call parity does not apply in the same way and provides bounds instead.

Tags

# Under put call parity shouldnt the implied volatility for call and put for same strike and maturity be the same?


# Under put call parity shouldnt the implied volatility for call and put for same strike and maturity be the same?












If all of the other inputs into black scholes (divs/rates/time to maturity/strick/current price/etc) are all the same between two pairs of calls/put contracts on the same security, shouldn't the implied volatility be the same?

For example I see SPY and AAPL has having similar IV for ATM put and calls.

However, it seems like for NFLX and GME, the calls have slightly higher IV? Why is that? In some cases, I have seen the ATM puts command a higher premium (embedded financing cost of shorts, but why is the IV sometimes lower for those puts?)

## Answer by Alex (score 1)

https://quant.stackexchange.com/a/68972

Firstly, there is no put call parity for American exercise as Ivan notes, but parity can provide bounds

But for European options, The IVs are the same for calls and puts at the ATM forward strike. The IVs will not be the same for ATM spot unless the forward equals spot. For stocks with very high dividends and/or borrowing costs, the forward price can be very different than the spot.

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