# 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.

• Another Question: Suppose the option exercised is a call with delta 0.75 (according to my model). If I consider market lot of 100, what is my obligation? Do I need to give delivery of equity if its physically settled or is my account debited by the LTP/Settlement price in case it is cash settled? – nimbus3000 Mar 18 at 7:40

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.

• I can know if I've been assigned the early excerise (since I was short) only at the end of the trading window, I wont be able to exercise my option. I can build a probability model around it if can see at real time how many options are exercised, but I'm not sure if that is the case. – nimbus3000 Mar 18 at 7:44
• ok I see... thought there may have been time to turn around and assign someone else – ZRH Mar 18 at 7:46

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.

• I'm not sure I understand this: 'Your delta hedge has made the same P&L whether exercise occurs or not.' I mean if I am delta hedged to start with, short ITM Call/Long corresponding OTM Put and hedged with futures then I lose my delta hedge with I'm assigned an early exercise. Agreed that I make on time value and have long gamma now, but I also have significant delta exposure which can leave me with a bloody nose, especially if there is a news flow between market close and exercise window. – nimbus3000 Mar 18 at 18:35
• Only if your option is cash settled, then yes, the early expiry removes your delta, but equity American options are physically settled. Once exercised it essentially becomes a forward contract which has 100% delta. – Ivan Mar 18 at 20:34
• I'm sorry I still dont understand this entirely. Say I have short call/long put position which i have hedged with long equity. So delta is zero. Now if I am assigned an early exercise under physical settlement, I would have to give delivery of equity. Hence, I am left with only a long put position the next morning. I do make money on time value, but I am left with delta exposure and long gamma. Is my understanding correct? – nimbus3000 Mar 19 at 10:43
• Yes. You can sell the put option outright, and collect whatever premium you can get. Or you can hedge it , which would mean buying some delta. In that case you would be long gamma going forward. – dm63 Aug 15 at 23:03