Options on stocks and ETFs in the US are American style: the owner can exercise on any trading day, not only at expiration. The binomial tree back in Module 3 prices that right; this lesson is about when to use it. That right sounds valuable, and it is, but a beginner uses it far too often. Most of the time exercising early throws money away. This lesson is about the two cases where it does not, and the two numbers on the chain that tell you when you are in one.
Alive is worth more than exercised
An in-the-money call is worth its intrinsic value plus its time value. Exercise it and you get the intrinsic value only; the time value is gone. On top of that you pay the strike today instead of at expiration, so you also give up the interest on that cash. Take a $150 call on a stock at $170 with 40 days left, quoted at $21.00. Intrinsic value is $20.00, so a dollar of time value is left. Exercising hands over $150 now to collect $20 of value, when selling the call collects $21. The rule is simple: a call with any time value left is worth more sold than exercised.
Holding the call instead of the shares keeps the strike earning interest and keeps a floor under you: if the stock collapses, the call stops at zero while shares keep falling. That floor is worth what a put at the same strike costs. Exercising gives up both.
The dividend exception
The one thing a call owner cannot collect is the dividend. On the ex-dividend date the stock opens lower by roughly the dividend, and the call drops with it, while the shareholder banks the cash. So the day before the ex-date there is a real choice. If the dividend is bigger than the time value left in the call, you are better off exercising, taking the shares and collecting the dividend. If the time value is bigger, keep the call. For a $0.50 dividend and a call with $0.20 of time value, exercise. With $1.00 of time value, hold. Only deep in-the-money calls with little time left usually pass this test, which is why early exercise of calls clusters on the day before an ex-date.
Time value of a $100 call against the stock price, with a 3% dividend yield. Deep in the money the lines dip below zero. Set the yield to 0% and they stay above it; raise the rate and they climb back. The model spreads the dividend smoothly over the year, where real ones arrive in lumps, so treat the depth as a guide.
Below zero, the model's call, which can only be exercised at expiration, is worth less than its intrinsic value. A real US stock call cannot trade there, because the holder would exercise before the ex-date and take the difference.
The put case
Puts run the other way. Exercising a put brings in the strike today, and cash today earns interest. A deep in-the-money put on a stock that has fallen hard may have almost no time value left, because there is little chance the stock moves enough to matter. If the interest you would earn on the strike over the remaining days is more than that sliver of time value, exercise. A $100 put on a stock at $60 with 60 days left and a 4% rate has about $0.66 of interest at stake; if the put quotes at $40.05, the five cents of time value is not worth waiting for. A dividend before expiration pushes the other way, since the stock will drop by it, so put owners tend to wait until the ex-date has passed.
A $100 put with 180 days left at a 6% rate, against the dashed line of intrinsic value. Hover at a stock price of $60: the solid line is under the dashed one. Drag the rate to 0% and the gap closes; with no interest to earn there is no reason to exercise early.
These charts use the European model, for options exercisable only at expiration. Deep in the money its put is worth less than intrinsic value, because it waits for a strike worth less today than the strike. The real, American put cannot fall below intrinsic value, since the owner can exercise and take the full strike now. The gap between the model's price and the dashed line is the least extra an American put is worth, part of what is called the early-exercise premium.
Time value of a $100 put against the stock price, from the European model. Below zero is the stretch where an American holder exercises, and how far below is the early-exercise premium. Raise the rate and the crossing point moves toward the strike; set it to 0% and it never comes.
Read it from right to left. Near the strike, time value is large: hold. As the stock falls, the chance of a rebound shrinks and the interest on the strike takes over until the line crosses zero. Past that point an American holder exercises, because waiting costs more in interest than the remaining upside is worth.
What to check on the chain
Two numbers settle it. The first is the time value of the contract: the mid price minus the intrinsic value, where intrinsic value is the stock price minus the strike for a call and the strike minus the stock price for a put. At deep in-the-money strikes this comes out at a few cents or at zero. A put quoted at exactly its intrinsic value is one the market already expects to be exercised. The second is the dividend: the next ex-date and the amount. If the ex-date falls before expiration and the amount is bigger than a call's time value, that call is a candidate the day before, and whoever sold it should expect to be assigned then.
The maths: the two early-exercise conditions
For European options on a stock with a dividend D going ex before expiration, parity rearranges into a formula for the call's time value, the price minus the intrinsic value: C - (S - K) = P + K(1 - e^(-rT)) - D. Here P is the put at the same strike, the floor, and K(1 - e^(-rT)) is the interest on the strike over the T years left. Exercising the day before the ex-date wins only when D > P + K(1 - e^(-rT)): the dividend has to beat the interest and the floor together.
Worked example for a call: strike $100, stock $130, 4% rate, a $0.60 dividend tomorrow. With 30 days left, 100 × (1 - e^(-0.04 × 30/365)) = 100 × (1 - e^(-0.00329)), about $0.33, and a $100 put with the stock at $130 is worth close to nothing. $0.60 beats $0.33, so exercise. With 120 days left the interest is 100 × (1 - e^(-0.01315)), about $1.31, which beats the dividend: hold.
For puts, with no dividend, parity gives P - (K - S) = C - K(1 - e^(-rT)). Exercise pays when the interest on the strike beats the call at the same strike, the only upside a put holder gives up. Strike $100, stock $60, 60 days, 4%: the interest is 100 × (1 - e^(-0.00658)), about $0.66, while a $100 call with the stock at $60 is worth a fraction of a cent. The European put is worth about $39.34, below its $40 intrinsic value; exercising takes the $40 and banks the interest.
Your turn
Open the AAPL chain, find a call about 5% in the money and read off its time value. Then open Dividend Analytics for the next payment. Finish on XLE with the same check on a put, and decide whether exercising it would give anything up.