delta of a call vs put (ex-div

Simplified put-call parity stipulates {{ call =~= put + underlier }}. PCP holds true whether underlier (say MSFT) spot is $20, $22.2 or whatever. Remember delta is always measured with tiny changes around a particular value of underlier SPOT price, so let’s assume MSFT spot price is now $20 ,

delta(call) =~= 1 + delta (put)

(You derive this by taking the first derivative of each item in the equation.)

Since delta(put) is always negative, you can see that given identical strike prices, the _magnitude_ of delta(call) + delta(put) is roughly 100%. — worth remembering.

There’s a bit of tricky fine print for the undaunted. In reality, the 2 magnitudes sometimes add up to exceed 100% for American options. I was told the key reason is early exercise [2]. Since the 2 options have identical strikes, exactly one of them is ITM. Just before dividend, the ITM option (either the put or the call) would have a higher delta thanks to the dividend. If 99% of the players in the market agree this ITM should be early exercised due to the dividend, then IMHO 1 lot of this ITM option feels like equivalent to 100 shares of MSFT, either long or short. Therefore delta of the ITM is similar to 100%.

Q: on the day before ex-dividend day, does the ITM option’s delta approach 100%?
A: I was told yes.

[2] there are other reasons like interest rate.

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Posted in PCP

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