delta of a stock option – on last days

For any call/put option
– ATM options (call or put) have delta close to 50%, so ATM option’s MV moves about 50c when underlier moves $1. [3]
– Deep ITM options have delta close to 100% (“100 delta”) , so it feels like a regular stock [1];
– Deep OTM options have delta close to 0  (“0 delta”). [2].
– Therefore, a trader uses magnitude of delta as approximate likelihood of expiring ITM. See P28 [[Trading Option Greeks ]]

You can see part of the reason in the curve of [Px (call option)  vs  spotPx(underlier) ] on P276 [[complete guide to cap mkt]]. ITM call’s slope is almost parallel to slope of a long stock. OTM call’s slope is nearly flat.

Before reading further, remember a trader observes fluctuations in underlier and in volatility level. Forgive my long-winded reminder – within an hour on the expiration day, market could exhibit a sudden increase in implied-volatility. New vol will impact delta, valuation, unrealized PnL.. until you exit.

My friend Chuck Kang, who traded options before, described that just before expiration (like the Triple-witching), option *premiums* jump wildly in response to underlier price moves. I can understand why in the case of a ATM option on a fairly volatile stock.

However, P31 [[Trading Option Greeks]] suggests that On the last days deltas diverge from 50% towards 100% or 0. The impending expiration pushes out delta.

[1] I feel timeVal doesn’t affect how _likely_ the option will expire ITM. A deep ITM is 99% sure to expire ITM, so a single lot of this option feels equivalent to 100 shares of underlier, either long or short. The MV consists of mostly intrinsicVal. Delta(intrinsicVal) is 100% for an ITM.

[2] I feel timeVal doesn’t affect how _likely_ the option will expire ITM. When underlier shifts up and down, the deep OTM option still shows no promise of expiring ITM. Delta(timeVal) is nearly zero. Delta(intrinsicVal) == 0 for an OTM.

[3] If an option is still ATM on its last days, then market doesn’t know whether it will expire ITM or OTM. Too close to call.


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