I'm not an options trader, but I have been digging around trying to learn what I can. This appears to be a good opportunity for me to risk embarrassing myself in public. Plus, I can gage how my learning process is coming along.
First, a buy-write is when you buy shares in the underlying and sell an option against those shares. That doesn't sound like the example you posted. And since you later indicated your question should assume an ITM naked Put, we'll go with that.
Using a SPY Put that is 2.33 points ITM as an example, and assuming no change in price, no upcoming ex-div date, and no change in IV, here's my take on this:
Looks like SPY closed at 413.67.
If you look at the 416 Put expiring on 9/16, the last traded price was 12.28. So had you sold that Put at that price, with the multiplier of 100, you would have brought in $1,228 in premium. The intrinsic value of that put is the strike minus the spot, so 2.33 points of intrinsic value, or $233. The extrinsic value is the premium minus the intrinsic, which is $995.
So had someone bought your 416 ITM Put and immediately exercised, they would be short 100 shares of SPY at 416 and be up the intrinsic value of $233. But since they paid $1,228 for your Put, they would actually lose the extrinsic value and be down $995 on the trade. No one is likely to do that, so your assignment risk is virtually non-existent.
Now ,if you look at that same 416 Put expiring on 8/10, it's a different story. The last traded price was 4.76, so $476. Intrinsic value has not changed and is still $233, but since it is much closer to expiration, the extrinsic value has shrunk from $995 to $243. Anyone exercising at this point would still be down the extrinsic value of $243 on the trade. Again, unlikely anyone would do that, so your assignment risk, albeit it higher, is still low.
Once extrinsic value is eliminated, that is where your assignment risk is high. That is why options traders often close their positions a week or so from expiration, while there is still enough extrinsic value in the option to mitigate assignment risk.
Naturally, price and IV are going to change, along with other variables, that is why it's important to keep track of intrinsic and extrinsic values -- to make certain intrinsic doesn't overcome extrinsic so you don't get caught with an unexpected assignment.
If that's not exactly correct, I hope I'm at least close. if not, maybe they'll have mercy on me.... and maybe even school me on my mistake(s). lol
