<<<1. Between liquid and ill-liquid options , which one has more chances of getting assigned ? ( with assumption that both puts are out of money)>>>
The odds of an out of the money put option being assigned are so low that it is not really worth worrying about. However, if the option is closer to the money it is usually more liquid and more likely to be assigned, so you could say a liquid option is more likely to be assigned than an ill-liquid option.
<<<2. Is there an estimate that could be found somewhere on - what percentage of out of money options are exercised?/ historical exercised option figures for an underlying equity>>>
Well under 1%. You could trade options every month for 20 years and never have it happen to you.
<<<3. Once assigned before expiration of an option that was written , can one buy the same option (if available) to close the written one to get away from assignment? or is there anything else that could be done to tackle assignment for minimizing the losses>>>
Once you have been assigned the trade of the underlying security has already taken place. You cannot use a "buy to close" transaction because the option no longer exists after exercise/assignment.
You cannot reduce a loss once it has occurred.
Some people would say you can reduce the loss by writing an offsetting option. (For example, if you bought shares because you received an assignment notice on a put you had written, you could write covered calls.) To me that is establishing a new position.
<<<4.Till what time on 3rd Friday of the month can one get assigned?>>>
Expiration does not occur until the Saturday following the 3rd Friday of the month, so you can be assigned on that Saturday.
You also need to understand that you never recieve an assignment when the market is open, so if you have not received an assignment by 9:30 a.m. Friday morning you will not receive an assignment any time on Friday.
<<<5.If you get assigned after trading hours on the 3rd Friday of the month, is there anything that could be done to cut losses?>>>
No. Once a loss has occurred it has occurred.
<<<6.For the option assignment process , does the OCC/Broker make distinction based on type of investor(retail vs institutional)>>>
No. The OCC picks the brokerage randomly. The brokerage must use a scheme approved by the OCC in picking an account. I believe the most common schemes are random selection and selection by the amount of time the option position has been open.
<<<7.Does the probability of getting assigned vary based on order size( 1 contract vs 50 contracts)>>>
If your brokerage selects the account to receive the assignment randomly, every option has the same chance. That means if your position is larger you have a better chance of getting an assignment notice.
If your brokerage selects the account to receive the asignment notice by some other method, the position size makes no difference.
From my experience, it is quite common to get partial assignments for deep in the money puts. For example, some months ago I wrote 150 Hovnanian (HOV) January $5.00 puts. Last week on Tuesday I was assigned 25 contracts. On Wednesday I was assigned 25 more contracts. The remaining 100 contracts remain open.
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Early assignment is not considered a bad thing by most option traders. When an option holder exercises options early, he essentially gives the option writer any time premium remaining.
Anyone who has written many put options in his life knows that deep in the money put options are frequently exercised early, so he should be prepared for early assignment. If he is experienced, he probably has offset much of his risk before the option is likely to be assigned.