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BOX SPREAD

The box spread, or long box, is a common arbitrage strategy that involves buying a bull call spread 

together with the corresponding bear put spread, with both vertical垂直的 spreads having the same

strike prices and expiration dates. The long box is used when the spreads are underpriced in relation to

their expiration values.

Box Spread (Long Box) Construction

Buy 1 ITM Call

Sell 1 OTM Call

Buy 1 ITM Put

Sell 1 OTM Put

LIMITED RISK-FREE PROFIT

Essentially, the arbitrager is simply buying and selling equivalent 相等的 spreads and as long as the

price paid for the box is significantly below the combined expiration value of the spreads, a riskless profit

can be locked in immediately.

Expiration Value of Box = Higher Strike Price - Lower Strike Price

Risk-free Profit = Expiration Value of Box - Net Premium Paid

Box Spread (Long Box) Payoff Diagram

EXAMPLE

Suppose XYZ stock is trading at $45 in June and the following prices are available:

• JUL 40 put - $1.50

• JUL 50 put - $6

• JUL 40 call - $6

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• JUL 50 call - $1

Buying the bull call spread involves purchasing the JUL 40 call(6) for $600 and selling the JUL 50

call(1.0)for $100. The bull call spread costs(5): $600 - $100 = $500

Buying the bear put spread involves purchasing the JUL 50 put (6) for $600 and selling the JUL 40

put(1.5)for $150. The bear put spread costs(4.5): $600 - $150 = $450

The total cost of the box spread is(9.5): $500 + $450 = $950

The expiration value of the box is computed to be(10): ($50 - $40) x 100 = $1000.

Since the total cost of the box spread is less than its expiration value, a riskfree arbitrage is possible

with the long box strategy. It can be observed 注意到 that the expiration value of the box spread is

indeed真正的 the difference between the strike prices of the options involved.

If XYZ remain unchanged at $45, then the JUL 40 put and the JUL 50 call expire worthless while both

the JUL 40 call and the JUL 50 put expires in-the-money with $500 intrinsic value each. So the total

value of the box at expiration is: $500 + $500 = $1000.

Suppose, on expiration in July, XYZ stock rallies to $50, then only the JUL 40 call expires in-the-money

with $1000 in intrinsic value. So the box is still worth $1000 at expiration.

What happens when XYZ stock plummets大跌 to $40? A similar situation happens but this time it is the

JUL 50 put that expires in-the-money with $1000 in intrinsic value while all the other options expire

worthless. Still, the box is worth $1000.

As the trader had paid only $950 for the entire box, his profit comes to $50.

COMMISSIONS

As the profit from the box spread is very small, the commissions involved in implementing 实现 this

strategy can sometimes offset all of the gains. Hence 因此 , be very mindful 留心的 about the

commissions payable when contemplating打算 this strategy. The box spread is often called an alligator 

鳄鱼 spread because of the way the commissions eat up the profits!

SHORT BOX

The box spread is profitable when the component组成的 spreads are underpriced. Conversely相反的,

when the box is overpriced, you can sell the box for a profit. This strategy is known as a  short box.