When Apple's share split 7 for 1 this weekend, the stock and the corresponding option prices will be adjusted accordingly. For every share of Apple stock you own, you'll get 7 shares, but the share price is divided by 7, so like Tim Cook said during the annual meeting two years ago, a stock split does nothing to the value of the stock.... Or does it?
When the share price is divided by 7, the stock options' strike price are also divided by 7 and the result will be peculiar: For example, a June 13 2014 Call option with $645 strike price representing 100 AAPL shares will be converted to 700 shares at the strike price of $92.14. Well, if you divide 645 by 7, you actually get $92.1429 (92.142857 to be more exact). This leaves $0.0029 "on the table" if you are a short this call because if your counter-party decides to exercise this call and make you sell your 100 shares, you will get $92.14, instead of $92.1429. Rounding error, you say? I'd call it an arbitrage opportunity because that $0.0029 rounding error is then multiplied by 700 shares, or $2.03 per contract.
In the financial world, traders (i.e. scalpers & high frequency traders) would gladly scalp pennies on the bid-ask spread all day long but for them that is still risky because the stock can move away from the price they are scalping at any time. So, if there is a way to scalp without taking on any risk, that is called arbitrage, and I contend that this rounding error is an arbitrage opportunity for those who have millions of dollar to trade.
Apple closed at $645.57 today and the last trades on the $645 call was 9.75 bid/9.9 ask while the $645 put was $9.1 bid/9.2 ask.
So let's say we can create a "short-around the box" position: sell AAPL at $645.60, sell "covered put" at 9.2 and buy "protective call" at 9.8 for a new proceed of $645. What this does is to ensure that you will (have the right AND the obligation to) buy AAPL at 645 on or before June 13... a wash with $0 profit.
Now comes Monday, these position becomes 700 shares of AAPL at $92.228, our long call becomes the right to buy 700 shares at 92.14 while our short put becomes the obligation to sell 700 shares at 92.14. But remember, it really should have been 92.1429 so you automatically gained 0.0029 x 700 or $2.03.
The $2.03 per contract "windfall" may not sound like much, but if let's say you have $6.456 Million to establish 100 (pre-split) positions of $64,560 each, that is $203 of riskless arbitrage.
This type of trade cannot be profitably done by retail investors due to the cost of brokerage commission and the precise price in which the three-legged position must be simultaneously obtained.
But as an "academic" example, it does illustrate that on Wall Street, there are pennies on the road to be picked up by those who notices it.
Disclosure: I am long AAPL.
Additional disclosure: I also long calls and hedged with puts on AAPL.