# Stock options: payoff diagrams assume European style exercising

Most literature on stock option strategies expresses payoff outcomes in terms of European options -- namely, ones that can only be exercised on the expiration date.

See this Iron Condor payoff diagram for example (with long put @ 35, short put @ 40, short call @ 50, and long call @ 55):

Most options brokerages in the US have American-style options that can be exercised at any point before or during the expiration date. This means that for multi-leg option strategies, you could afford to lose more than these diagrams traditionally show.

In the above example, you could lose more than projected if the stock price reaches \$35 and \$55 at separate points before the expiration date, given that you haven't closed your open contracts when the stock hits either of the two prices. How do people usually handle this?

Actually you can't lose more than what the diagram shows, even with American options, and these diagrams apply to both types.

If the underlying stock gets to let's say \$35 before expiration and your short \$40 put gets assigned early (so you get 100 shares of stock from the put holder for cash outflow of \$4,000), you still can't lose more than \$400, because you still have the long \$35 put as hedge + the \$100 cash from net premium received.

If the stock ends up at let's say \$30 at expiration, you simply exercise your long \$35 strike put and sell the stock for \$35 = \$3,500 cash inflow. Loss on the stock is \$500, with your initial premium received when opening the iron condor total loss is \$400.

If you get assigned the \$40 put and hold the stock, and the market later turns and gets to \$55, and also your \$50 call gets assigned early, the assignment actually means you sell the 100 shares you now own (from the \$40 put assignment) to the call holder for \$50 = \$5,000 cash inflow = profit of \$1,000 on the stock (and you still hold the long options and keep the \$100 initial cash). So having both your short legs assigned early actually leads to a profit of \$1,000 + \$100 premium received. But of course this is virtually impossible in the real world, because 1) early assignment is unlikely as the person exercising the option would be giving up time value and 2) the stock getting both below \$40 and above \$50 is unlikely (though possible).

A case when you could lose more than \$400 is if you exercise your long put as price reaches \$35 (get a short position in the stock at \$3,500) and the stock turns around and goes up above the \$40 strike. But you don't need to (and should not) exercise. As the option's holder you have the right, but not obligation to exercise.

Generally, any action - exercising early, selling options, or buying additional options - that you do can change the payoff diagram and change your maximum profit/loss, but any action someone else does - you get assigned early - does not.

I'm not sure from your question that you understand the position correctly: With iron condor, you are long the outer strikes (\$35 put and \$55 call) and can't get assigned on these, because you are long. Only you can exercise these. You can only be assigned the short middle strikes (\$40 put and \$50 call), and if that happens you are hedged by the long outer strikes, so maximum loss never exceeds what the diagram shows. If you, theoretically, happen to get assigned both the middle strikes, you actually gain the difference, because you effectively buy the stock at the lower strike and sell the stock at the higher strike.

In sum, even with American options, don't worry about early assignment. You can't lose more than \$400, unless you do something stupid (exercise your long options early while keeping the shorts open).

It is very rarely optimal to exercise an American option before expiry. Even if the stock goes close to 0, the market value of the options would likely still be slightly higher than the intrinsic value, so it would not be optimal to exercise since you could sell it for more than the exercise payoff.

All that to say that the payoff at expiration would be the same for American and European options, and there's no simple way to account for the difference between American and European options before expiry.

How do people usually handle this?

I suppose if any of your option legs were exercised early, you could just take the proceeds (the price paid for the stock for a call, or the proceeds from selling the stock you received for a put) and buy a new option to take it's place. I do not know of any brokers that would automatically make your basket whole again in that scenario, likely because it is extremely rare.

• (1) Your last paragraph needs a bit of cleaning up. If the short call is assigned early, you receive cash for the short stock sale and if the short put is assigned early, you pay cash for the long stock purchased. If one closed the equity position, one would then sell (not buy) a new option to restore the original position. (2) Discount and Dividend Arbitrage can lead to early exercise of ITM options. Sep 22, 2018 at 17:08