Managing Overnight Assignment Risk in American Calls
Summary
The document discusses a market maker who is assigned an in-the-money American call after the underlying market closes, creating stock delivery and delta exposure by the next open. Because the underlying cannot be traded during that interval, the direct delta hedge cannot be adjusted overnight. One proposed way to avoid carrying the resulting position is to hold an exercisable in-the-money American call that can deliver shares.
The answers explain that early exercise does not create a risk worse than the short gamma already present in a delta-hedged short option. If the holder exercises suboptimally and gives up remaining time value, the short option position benefits; if exercise is optimal, the existing hedge should already reflect near-full delta. Any remaining share delivery can require buying the unhedged fraction, with some execution slippage, or borrowing shares when another option cannot be exercised to supply them. The discussion is qualitative and assumes liquid shares and a suitable offsetting option may be available.
Key ideas
- Exercise after the underlying closes prevents direct overnight adjustment of the delta hedge.
- An assignment changes share delivery obligations, while the core exposure remains the position’s short gamma.
- Suboptimal exercise can benefit the short option holder by surrendering time value.
- Share purchases or borrowing may be needed to complete delivery, with potential slippage.
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Full text
# American Option Exercise
# American Option Exercise
Suppose I am a market maker in American options. At end of day I have positions in various options but my portfolio is overall hedged. Now, after the market close, someone decides to exercise an ITM Call which is assigned to me. So, when the market opens next morning, I see that I have significant delta exposure in my portfolio. Can someone tell me how do I hedge against such an event. I have never traded or studied American options. So if my question seems a little elementary, please excuse.
## Answer by ZRH (score 1)
https://quant.stackexchange.com/a/44641
Given that exercise is possible after the underlying has stopped trading, you cannot hedge away your delta directly. Only way not to run with a position overnight is by having an American ITM call that you can in turn exercise.
## Answer by Ivan (score 1)
https://quant.stackexchange.com/a/44649
There is no additional hedge that you really need: if you are comfortable with being short the delta-hedged option and hence short gamma in the first place, nothing that can happen to you in this scenario is worse than could happen without exercise. Your “problem” is your short gamma, not the early exercise.
In fact you will make a significant windfall gain if the holder has exercised suboptimally and forfeited his time value. For any spot price you can consider tomorrow at open, the value of your short option is now equal to or less than it would otherwise have been with an optimally-behaving holder. Your delta hedge has made the same P&L whether exercise occurs or not.
Where you incur a little slippage is in bringing the delta to 100%, from whatever you had as a hedge. If the exercise is optimal, then you should have had 100% anyway, which you now deliver. If not then you need to buy the extra $1-{\Delta}$ to deliver. If the stock is reasonably liquid, this cost is a tiny amount.
If your concern is that your exercised option is hedged with another option that you cannot exercise to get your hands on shares, then you will need to borrow said shares in size ${\Delta}$, buy the rest as above, and deliver that.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.