What is the relationship between Time-To-Expiry and Delta?

Question

Is there any regular relationship between Delta and the Time-To-Expiry of an option?

I have observed that options that expiry sooner are more sensitive to underlying movements (with equal strikes). Is there any way to justify this relationship?

I suppose that at some point as well as the options get's closer to the expiry it's delta will be much lower for deep-in-the money or deep-out-of-the-money option.

Answer 1

Here is a page from The Options Guide with an understandable picture.

They explain,

As the time remaining to expiration grows shorter, the time value of the option evaporates and correspondingly, the delta of in-the-money options increases while the delta of out-of-the-money options decreases.

This happens because the shorter expiration that is deep in-the-money tends to behave as the stock, with an underlying gain of $1 having an option movement of more than 95 cents (that's a delta > 0.95).

But with a shorter expiration, the out-of-the-money option has very little chance of being exercised. Thus, the option movement is small, perhaps 5 cents (that is, a delta around 0.05).

Answer 2

You are looking for the Greek commonly referred to as Charm. This is a quick visualization with a good chart I found on Google:

https://www.optiontradingtips.com/greeks/charm.html

Answer 3

Yes, the 'delta' has correlation with 'theta'. It is called 'second-order greek Charm' . For OTM options, the delta in last few days of trading is approaching 0(zero), while for ITM options delta approaching 1(one) in last few days of trading. here few examples: example_1: price of underlying = $100, strike = 110, interest rate = 1, implied volatility = 100 . (out of the money call option)

example_2: price of underlying = $100, strike = 90, interest rate = 1, implied volatility = 100 . (in the money call option)

more details could be found at this article: https://optionstrade.info/delta-vs-time-decay/