Why would anybody exercise early a DITM ES option?

No dividend. Enough liquidity to sell the option at a good price.
I don't see why anybody would sacrifice time value, increase their margin and pay commission while they could just wait the option expiration.

Any idea?

 

They need it for a hedge and don't want to keep losing on the premium

 

Delete that while you still can.

 

I assume you were the benefactor of said gift. Happens all the time. Not sure what strike we are talking about, or how much extrinsic is in the option, but sometimes people buy options directionally, have them go their way, then just exercise the option instead of liquidating it or hedging it. Some things you don't seek reason for, just smile and say thanks.

 

No. It was 4 am or something.

 

Also, let's say you have a DITM call option with strike at K and currently, the price is of the underlying is S with S > K. The intrinsic value of your option then is:

I = S - K

If P is the premium paid, then the price of your call option is:

C = P + I

Let's say you bought the option for a hedge and you are now expecting the price of the underlying to decline by $s where s > S-K (so still DITM). So the new value would be:

I = (S - s) - K
C = P + (S - s) - K

But P has also declined:

C = (P-p) + (S-s) - K

In order for you to maintain the right hedge, you might decide exercise so you don't lose p+s in exposure.

I retain the right to say I have been up since 3am.

 

I see.
Yes say thanks unless this option is part of a combo and that can cause some trouble. Then have to quickly react.

 

I had difficulties with this:

My mind kept telling me s=0, s=0... while I was reading the rest.

You're basically saying that when the markets goes down, your DITM call despite being still DITM won't hedge as well as before (delta decreasing) so you could prefer exercising. It makes sense.
Depending on what's cheaper, you could exercise or be selling this option and buying 1 another at a lower strike price.

Nice maths at 3am!

 

Yep, exactly.

Haha, I will take the compliment.

 

I'm a bit puzzled. Your hedge and your option premium should move in opposite directions, right? Also, why wouldn't you simply adjust the hedge by buying or selling more of the underlying as the price moves? Given the associated changes in gamma, seems like you'd be making money in either direction. By exercising early, it seems like you'd be throwing away all the extrinsic you've paid for.

(I'm brand new to figuring this stuff out, so I'm not making any assertions - simply wondering what I've missed.)