Box Spreads or Box Arbitrage is a strategy involving the combination of a Bull Spread and a Bear Spread. This strategy can be implemented in two ways, either by combining a Call Bull Spread and a Put Bear Spread, or by combining a Put Bull Spread and a Call Bear Spread.

This strategy implies that the payoffs are the same regardless of whether the price of the underlying asset rises or falls. Indeed, the payoffs will be equal to K2 – K1 regardless of where the spot is at the expiry of the options. The initial value of the Box Spread must therefore always be equal to the current value of K2 – K1. If there is not a match between K2 – K1 and the current value of the box spread, there is an arbitrage opportunity. For example, if the Box Spread costs less than K2 – K1, you will have to buy it, on the other hand, if the Box Spread costs more than K2 – K1, you will have to buy the symmetrical strategy to benefit from arbitrage.

The payoffs of the strategy combination are illustrated below:

For example, ABC stock trades for \$50. Each options contract in the four legs of the box controls 100 shares of stock.

– Buy the 49 call for \$3 (ITM) for \$300

– Sell the 53 call for \$1.25 (OTM) for \$125

– Buy the 53 put for \$2.50 (ITM) for \$250

– Sell the 49 put for \$1 (OTM) for \$100

The total cost of the trade (before commissions and fees) would be \$300 – \$125 + \$250 – \$100 = \$325. The spread between the strike prices is 53 – 49 = 4 (K2 – K1).

Multiply by 100 shares per contract = \$400 for the box spread.

In this case, the investor can lock in a profit of \$75 (\$400 – \$325). That is a nice margin, and this is only when the net cost of the box is less than the expiration value of the spreads, or the difference between the strikes K2 and K1.