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Option Greeks

Box Spread

The last strategy that we will learn is a ‘Box Spread.’


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


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


However, such discrepancies are so short-lived and marginal that it is hard to execute a Box Spread fast enough. Box spreads should be used when one detects a violation of Put Call Parity. Put Call Parity is violated all the time in the market. But most of these violations are so insignificant that an arbitrage opportunity does not exist when commissions are involved. There are many ways to test for a significant violation of Put Call Parity and such profitable opportunities are so rare and tend to fill out so quickly that softwares are used to detect and execute the spread.


Box spreads open up an arbitrage opportunity without the use of the underlying itself. There are two types of Box spreads:

  • Long Box Spread 
  • Short Box Spread

A long box spread includes buying a bull call spread with a matching bear put spread. These vertical spreads must have the same strike prices and expiration dates.


So 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 of the ITM call and OTM put must be the same. Similarly, strike price for the OTM Call and ITM put must be the same. This results in a position that looks like the table below:



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

The above table clearly shows that the Box Spread is a combination of a Bull call spread and a Bear put spread across the same strike prices. Another way of understanding box spread is that it is actually a combination of a Synthetic Long Stock and a Synthetic Short Stock.


A bullish vertical spread maximizes its profit when the underlying closes at the higher strike price at maturity. The bearish vertical spread maximizes its profit when the underlying closes at the lower strike price at maturity. By combining both the bull call spread and the bear put spread, a trader removes the risk of the price of underlying at the expiry. This is so because the payoff is always the difference between the two strike prices at the time of expiry.


If the cost of the spread is less than the difference between both the strike prices, then the trader has locked in a risk-free profit also making it a delta-neutral strategy. Otherwise, the trader has incurred a loss which is the cost to execute this strategy.

  • Box value (at expiration) = Higher strike price – Lower strike price
  • Maximum Profit = Box Value – Net premium paid
  • Maximum loss = Net premium paid

Once the Box Spread is executed, you will have to wait till expiration and then close the position for the profit pocketed. A short box spread can be used when the net debit is higher than the expiration value. A Short Box Spread is just reversing the buys and sells of a long box spread.


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