What are the odds of being assigned for a long dated in-the-money call option?

Question

If I sell a 2-year future dated call option that is slightly in the money (For example if Citi today is $5.13, I sell a call option for strike price $5.00 at Jan 2013 - today is Jan 2011), what are the odds that I will be assigned in the next 60-90 days?

What about for a general well-traded stock?

Answer 1

The answer to your specific question is that the odds of that option being assigned (meaning the other guy exercises) are close to zero.

Looking at early exercise risk for call options more broadly:

An American-style* option should almost never be exercised early, especially if the underlying stock doesn't pay a dividend. There are a lot of ways to explain why this is, but below are the easiest ones, both of which approach the problem from the perspective of the "other guy" who owns the options, since they're the one deciding whether to exercise or not. For simplicity, the initial explanations assume the stock has no dividend.

[* "American-style" simply means that the option can be exercised prior to the expiration date; "European-style" options can only be exercised at expiration. All standard, listed options on individual stocks are American-Style]

If you're not planning to keep the stock you buy when you exercise a call option, but instead intend to sell the stock right away, you're almost always better off just selling the call option. A call option's value is made up of two components.

Call Value = Intrinsic Value + Time Value

The intrinsic value is simply the amount by which the stock's current price is higher than the call strike - it's the current discount to the stock's price that you get if you exercise the call, thereby purchasing the stock at the strike price. So, if the intrinsic value were the total value of the option, the price you could get for selling the call would be the same as what you'd make by exercising the right to buy at the strike price, and then selling the stock at its current value. But that's the least that the call should be worth, since the call's value is that amount plus the time value. Time value is far more complex to calculate, but for this discussion, it's enough to know this: it can't ever be negative. So, at best, exercising a call early and then selling the stock means throwing away the time value of the option, so in those rare cases where time value is zero, it should be a wash to exercise and sell, and in all other cases, you'd be worse off, since you'd only capture the intrinsic difference between the stock's price and the strike price.

If you are planning to keep the stock after you exercise, you could still apply the same argument: Assuming there is some time value, you'd be better off selling the call and then buying the stock at its current price than you would by exercising. (You'd have net saved the amount of the time value). But here's a simpler way to look at it in this case:

Even if you plan to keep the stock long term, exercising early is effectively locking in the worst possible price you could have to pay to buy it.

So, in the Citi example, the call owner is guaranteed the right to buy the stock at $5 for two years. If the stock goes to $100, he or she can still buy it at $5, so he can't possibly pay more than $5 until the option expires. But if the stock should drop lower, say to $4, or $3, he can buy it at that price rather than $5. So, by exercising the option, the call owner is essentially trading the ability to buy the stock for $5 or lower for the ability to buy it at $5.

So, for underlying stocks with no dividend, it is generally considered irrational to exercise an option early, assuming you like money.

There are a couple of key exceptions, the latter of which is more relevant:

• Irrational exercise is possible, but very, very rare. It's always possible that someone who hates money or math could exercise the option, but this is extremely unlikely - money will flow quickly into irrational markets and generally ensure that almost all positions with easily calculated values are owned by entities that can calculate them.
• Poor option liquidity relative to that of the stock can complicate matters. If the options market is so illiquid that you have to sell your call for less than the intrinsic value after you account for the bid-ask spread, it could be slightly less cost-effective to sell an option with no time value than to exercise and sell the stock. However, this is pretty rare, since it requires all of the following: A) the option has little or no time value, B) the options are very illiquid, and C) the stock is decently liquid. And B) and C) are generally not likely to both be true, as the stock's liquidity will usually inform the option's.
• The time value is close to zero and a dividend is being paid. Generally speaking, the only time a rational actor will exercise a call option early is when a dividend is about to be paid, and the value of that dividend is higher than the call option's current time value. Without getting into complex option pricing, this gets the crux: the owner of a call option does not capture the value of a dividend payout, so in those cases where an option is so deep-in-the money and/or close enough to expiration that the time value is below the dividend about to be paid, it makes sense to exercise just before the dividend's ex-date.

The math gets a little tricky here, but here's a neat trick to at least let you know if you should be worried: The value of the put option with the same strike and expiration is a quick and dirty proxy for the time value of the call. So, if you're trying to figure out if you're at risk for assignment due to a dividend, and you're too lazy to back the intrinsic value out of the call's current value, just look at the put: In the Citi example, it's the put with a 5 strike and the same expiration date. Since that put's value is roughly the same as the time value of the call we have, we can just compare it to the dividend amount. if the put's value is about the same or lower price as the dividend, you could be at risk for early assignment.

Answer 2

Uh, better than zero. There is a point where the position is deep enough in the money that the time value is less that the dividends the option buyer is giving up. I've had calls exercised on me for this very reason.