During the life of an American option many events can occur in which it might be preferable to own the underlying shares (rather than the option) and exercise early.In addition to dividends, an investor might want the voting rights, or alternatively might want to sell the option to purchase another option (rolling the option). We investigate these life cycle events and explain when it is in an investor’s interest to exercise, or roll, an option before expiry.
Converting options early is Rare
Options on indices are usually European, which means they can only be exercised at maturity. The inclusion of automatic exercise, and the fact it is impossible to exercise before maturity, means European options require only minimal maintenance. Single stock options, however, are typically American(apart from emerging market underlyings).
While American options are rarely exercised early, there are circumstances when it is in an investor’s interest to exercise an ITM option early. For both calls and puts the correct decision for early exercise depends on the net benefit of doing so (ie, the difference between earning the interest on the strike and net present value of dividends) versus the time value of the option.
* Calls should be exercised just before the ex-date of a large unadjusted dividend. In order to exercise a call, the strike price needs to be paid. The interest on this strike price normally makes it unattractive to exercise early.
However, if there is a large unadjusted dividend that goes ex before expiry, it might be in an investor’s interest to exercise an ITM option early (see Figure 4 above). In this case, the time value should be less than the dividend NPV (net present value) less total interest r (=erfr×T-1) earned on the strike price K. In order to maximise ‘dividend NPV– Kr’, it is best to exercise just before an ex-date (as this maximises ‘dividend NPV’ and minimises the total interest r).
* Puts should be exercised early (preferably just after ex-date) if interest rates are high. If interest rates are high, then the interest r from putting the stock back at a high strike price K (less dividend NPV) might be greater than the time value. In this case, a put should be exercised early. In order to maximise ‘Kr – dividend NPV’, a put should preferably be exercised just after an ex-date.
- Figure 4. Price of ITM and ATM Call Option with Stock Price over Div Ex-Date:
Calls should be exercised early if there is a large dividend
The payout profile of a long call is similar to the payout of a long stock + long put of the same strike . As only ITM options should be exercised and as the strike of an ITM call means the put of the same strike is OTM, we shall use this relationship to calculate when an option should be exercised early.
An American call should only be exercised if it is in an investor’s interest to exercise the option and buy a European put of the same strike (a European put of same strike will have the same time value as a European call if intrinsic value is assumed to be the forward).
* Choice A: Do not exercise. In this case there is no benefit or cost.
* Choice B: Borrow strike K at interest r (=erfr×T-1) in order to exercise the American call. The called stock will earn the dividend NPV and the position has to be hedged with
* -Kr + dividend NPV – time value > 0
* dividend NPV - Kr > time value for American call to be exercised the purchase of a European put (of cost equal to the time value of a European call).
For puts, it is simplest to assume an investor is long stock and long an American put. This
payout is similar to a long call of the same strike. An American put should only be exercised against the long stock in the same portfolio if it is in an investor’s interest to exercise the option and buy a European call of the same strike.
*Choice A: Do not exercise. In this case the portfolio of long stock and long put benefits from the dividend NPV.
* Choice B: Exercise put against long stock, receiving strike K, which can earn interest r (=erfr×T-1). The position has to be hedged with the purchase of a European call (of cost equal to the time value of a European put).
* Kr – time value > dividend NPV
* Kr – dividend NPV > time value for American put to be exercised
Selling ITM options that should be exercised early can be profitable
There have been occasions when traders deliberately sell ITM options that should be
exercised early, hoping that some investors will forget. Even if the original counterparty is aware of this fact, exchanges randomly assign the counterparty to exercised options. As it is unlikely that 100% of investors will realise in time, such a strategy can be profitable.
ITM OPTIONS USUALLY EXERCISED AUTOMATICALLY
In order to prevent situations where an investor might suffer a loss if they do not give notice to exercise an ITM option in time, most exchanges have some form of automatic exercise. If an investor (for whatever reason) does not want the option to be automatically exercised, he must give instructions to that effect. The hurdle for automatic exercise is usually above ATM in order to account for any trading fees that might be incurred in selling the underlying post exercise.
Eurex automatic exercise has a higher hurdle than CBOE
For the CBOE, options are automatically exercised if they are US$0.01 or more ITM (reduced in June 2008 from US$0.05 or more), which is in line with Euronext-Liffe rules of a €0.01 or GBP0.01 minimum ITM hurdle.
Eurex has a higher automatic hurdle, as a contract price has to be ITM by 99.99 or more (eg, for a euro-denominated stock with a contract size of 100 shares this means it needs to be at €0.9999 or more). Eurex does allow an investor to specify an automatic exercise level lower than the automatic hurdle, or a percentage of exercise price up to 9.99%.