Box Spread - The Box Spread

The Box Spread

Now consider the put/call parity equation at two different strike prices and . The stock price S will disappear if we subtract one equation from the other, thus enabling one to exploit a violation of put/call parity without the need to invest in the underlying stock. The subtraction done one way corresponds to a long-box spread; done the other way it yields a short box-spread. The pay-off for the long box-spread will be the difference between the two strike prices; and the profit will be the amount by which the discounted payoff exceeds the net premium. For parity, the profit should be zero. Otherwise, there is a certain profit to be had by creating either a long box-spread if the profit is positive or a short box-spread if the profit is negative.

The long box-spread comprises four options, on the same underlying asset with the same terminal date. They can be paired in two ways as shown in the following table (assume strike-prices < ):-

Reading the table horizontally and vertically we obtain two views of a long box-spread.

• A long box-spread can be viewed as a long synthetic stock at a price plus a short synthetic stock at a higher price .

• A long box-spread can be viewed as a long bull call-spread at one pair of strike prices, and, plus a long bear put-spread at the same pair of strike prices.

We can obtain a third view of the long box-option by reading the table diagonally. In order to interpret the diagonals we need to introduce the straddle, which is a combination of a long call and a long put both at a strike price equal to the current stock price (at-the-money). This combination is direction neutral, its terminal payoff being dependent not on the direction of movement of the stock price but only on the magnitude of the movement. The band between the break-even points can be extended by separating the strike prices of the two options symmetrically with respect to the current stock price:-

• If both options are in-the-money the combination is called a long gut.
• If both options out-of-the-money the combination is called a long strangle.

Returning to the long box-spread, we see that the leading diagonal is a long gut combination, and the other diagonal is a short strangle combination. Hence a long box-spread may be created as a coupling of a long gut with a short strangle.

The short box-spread can be treated similarly.