Box Spread


Box Spread - Definition


The Box Spread is a complex 4 legged options trading strategy designed to take advantage of discrepanies in options prices for a risk-free arbitrage.


Box Spread - Introduction


A Box Spread, or sometimes called an Alligator Spread due to the way the commissions eat up any possible profits, is an options trading strategy used to exploit price discrepancies in order to reap a risk-free arbitrage.

Such situations occur when the principle of Put Call Parity is violated by strong, short term demand shifts in the options market. When such a situation occurs, a Box spread can be used to "box in" the profit created by the imbalance.

However, such discrepancies are so short-lived and marginal that it is hard to put on a Box Spread fast enough to take advantage of it and that whatever profits there may be is so small that most of the time, it does not justify the commissions paid. That being said, the Box Spread remains one of the few true blue options arbitrage strategies to ever exist and still used amongst highly sophisticated Market Makers who can trade without the punitive commissions paid by retail investors.



When To Use Box Spread


Box spreads should be used when a significant violation of Put Call Parity is detected. Put Call Parity is violated all the time in the marketplace but most of these violations are so insignificant that no arbitrage opportunity exist when commissions are involved thus making the Box Spread ineffective. There are many ways to test for a significant violation of Put Call Parity and such profitable opportunities are so rare and tends to fill out so quickly that softwares are usually needed to detect it and then execute a Box spread.

A profitable options arbitrage opportunity for a Box Spread occurs when the expiration value of the Box Spread is higher than the net debit paid along with commissions. If the expiration value of the Box Spread is lower than the net debit paid along with commissions, a Short Box Spread should be used instead. When the integrity of Put Call Parity is strong, the expiration value of the Box Spread should equal the net debit paid allowing for no arbitrage opportunities. Most often, the breach in Put Call Parity is so weak that it barely covers the commission paid for such a position, that is why commissions need to be taken into consideration when exploring the possibility of a Box Spread.

Expiration value of Box Spreads is the difference between the strike prices used by the position multiplied by the number of contracts bought.

Box Spread Expiration Value Example :

Assuming XYZ trading at $55. Its options are:
Jan 50 Call : $7
Jan 50 Put : $3
Jan 60 Call : $2
Jan 60 Put : $7

Assuming only 1 contract of each option is used.

Expiration Value = (60 - 50) x 100 = $1000 per position


How To Execute Box Spreads


Box spreads opens up an options trading arbitrage opportunity without the use of the underlying stock itself and comes in 2 versions. Long Box Spread as well as the Short Box Spread. In general, the version to be used is the version that yields a positive profit.

A Box Spread consists of 4 options across 2 strike prices. They are:

Buy ITM Call + Sell OTM Call + Buy ITM Put + Sell OTM Put

Strike price for the ITM call must be the same as the OTM put. Likewise, strike price for the OTM Call must be the same as the ITM Put. This results in a position that looks like the table below:

Bull Call Spread Bear Put Spread
Synthetic Long Stock Buy Call @ X1 Sell Put @ X1
Synthetic Short Stock Sell Call @ X2 Buy Put @ X2

X1 = In The Money Strike Price
X2 = Out Of The Money Strike Price

From the table above, it is clear that the Box Spread actually consists of a Bull call spread and a Bear put spread across the same strike prices. Another way of looking at it is that the box spread is actually made up of a Synthetic Long Stock and a Synthetic Short Stock.

Here's the tricky part. Which 2 strike prices to choose for the position depends on which combination of strike prices produces an arbitrage opportunity. There are so many strike prices for some stocks that by the time you got to the one combination that produces an arbitrage, the price discrepancy would already have been closed off. That is why arbitraguers and large financial institutions uses softwares to search for such opportunities and to execute the option trades.

Long Box Spread Example :

Assuming XYZ trading at $55. Its options are:
Jan 50 Call : $7
Jan 50 Put : $3
Jan 60 Call : $2
Jan 60 Put : $7

Sell To Open 1 contract of Jan $60 Call at $2
Buy To Open 1 contract of Jan $50 Call at $7
Buy To Open 1 contract of Jan $60 Put at $7
Sell To Open 1 contract of Jan $50 Put at $3

Net Debit = [($7 - $2) + ($7 - $3)] x 100 = $900.00 per position

Expiration Value = (60 - 50) x 100 = $1000 per position

Maximum profit = $1000 - $900 = $100 per position

Since expiration value is higher than net debit, an arbitrage opportunity for a possible $100 profit per position exists assuming commissions are less than $100 per position.

Once the Box Spread is put on, all you have to do is to wait till expiration and then close the position for the locked-in profit. In case the net debit is higher than the expiration value, a Short Box Spread can be used instead with the same effect by expiration. A Short Box Spread is merely reversing the buys and sells of a long box spread.

Short Box Spread Example :

Assuming XYZ trading at $55. Its options are:
Jan 50 Call : $8
Jan 50 Put : $3
Jan 60 Call : $2
Jan 60 Put : $8

Buy To Open 1 contract of Jan $60 Call at $2
Sell To Open 1 contract of Jan $50 Call at $8
Sell To Open 1 contract of Jan $60 Put at $8
Buy To Open 1 contract of Jan $50 Put at $3

Net Credit = [($8 - $2) + ($8 - $3)] x 100 = $1100.00 per position

Expiration Value = (60 - 50) x 100 = $1000 per position

Maximum profit = $1000 - $900 = $100 per position



Trading Level Required For Box Spread


A Level 3 options trading account that allows the execution of debit spreads is needed for the Box Spread. Read more about Options Account Trading Levels.


Profit Potential Of Box Spread


Box spreads make in profit the difference between the net debit or net credit and the expiration value of the position no matter how the underlying stock moves.


Risk / Reward of Box Spread



Maximum Profit : Limited

Maximum Loss : No Loss Possible


Options Greeks Of Box Spreads



Box Spreads Greeks:

Delta: Neutral

Gamma: Neutral

Theta: Slightly Positive

The total delta and gamma of the put options cancels out the delta and gamma of the call options, creating a perfectly delta and gamma neutral position. This means that the value of the position will not change with any change in the underlying stock but will end up with a slight profit by expiration due to time decay.


Advantages of Box Spreads


:: Capable of risk-free profit


Disadvantages of Box Spreads


:: Extremely small profits sometimes does not justify the commissions paid
:: Extremely hard to spot and take advantage of such opportunities
:: Price discrepancies gets balanced off very quickly, making it hard to put on a position


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