If you’ve taken a college derivatives class, you must know about American and European ‘options’.
European options contracts can only be exercised at the expiry of the contract, while American options contracts can be exercised anytime after purchase (yay freedom!).
Now when and why would you exercise an American option before its expiry?
Short answer: As a general rule, you should early exercise an option when the current payoff of exercising the option is more than the value of the option. In other words, it is more profitable to exercise than to hold.
Long answer: Well, the decision depends on two things-
What is the option underlying (i.e. what do you buy/sell upon exercising)?
We will only look at options delivering stocks or futures.
Is it a call or a put option?
Case 1: Stock Options
When a stock option is exercised, you get credited/debited the full exercise price amount.
Case 1A: Call Options
Let’s take an American call stock option for instance. A call option’s value is made up of 4 parts
Call Stock Option Value = Intrinsic Value + Volatility Value + Interest Value - Dividend Value
Note that dividends decrease the value of a call option and hence dividend value is negative. This is because stock forward values decrease with dividends and call options to have a positive correlation (i.e. +ve delta) to the stock forwards (i.e. underlying).
Conversely, interest on the notional increases the value of the stock forward and hence interest value is positive in the above equation.
When we exercise an option we get the intrinsic value. So if the call option value falls below the intrinsic value, we can exercise the call option to get at least the intrinsic value.
Effectively, we will find it profitable to exercise an American call stock option when
Call Stock Option Value < Intrinsic Value
Dividend value - Interest Value > Volatility Value (using the above equation)
Another way to think about this is that when we convert a call option into a stock- we get the dividends on the stock and pay the interest on the notional value of the stock (i.e. we borrow money to buy stock)
Do we exercise immediately after the dividend Value exceeds the Volatility Value + Interest Value?
To answer that, let’s think about what happens if we exercise tomorrow instead of today- We lose 1 day of interest and volatility value and gain… nothing!
Our goal is to convert the Call position (which does not give us a dividend) into a stock position to gain the dividend (only if the above equation holds true of course).
So ideally, we should wait until the day before the ex-dividend date to exercise the call option. We can do it before that date (if the above relation holds true) but it won’t be ideal.
Case 1B: Put Options
For American put options delivering stock, the value equation is
Put Stock Option Value = Intrinsic Value + Volatility Value - Interest Value + Dividend Value
Note that Interest and Dividend values have flipped signs because a put option is inversely proportional (i.e. -ve delta) to the value of the stock forward.
Extending the above logic, you would only exercise a put option when
Put Stock Option Value < Intrinsic Value
Interest Value - Dividend Value > Volatility Value (using the above equation)
Based on the above condition, early exercise probably becomes the most profitable after the dividend value goes to 0 (i.e. ex-div date)
However, that is not necessarily true, the maxima of Interest Value - Dividend Value - Volatility Value could occur earlier as well (in high-interest rate, low volatility regimes).
Case 2: Futures Options
Options that deliver futures don’t require a credit/debit of the entire exercise price amount upon exercise. Instead, you get credited the difference between the exercise price and the current future price (i.e. the intrinsic value of the option).
Thus we will exercise a futures option if
Interest on intrinsic value > Volatility Value
Note that
As each day passes, we lose one day of intrinsic value and use one day of volatility value (theta).
Early exercise becomes profitable when one day of interest value is more than one day of volatility value.
i.e. |F - X| * r / 256 > theta.