In options trading, a box spread is a combination of positions that has a certain payoff, considered to be simply "delta neutral interest rate position". For example, a bull spread constructed from calls combined with a bear spread constructed from puts has a constant payoff of the difference in exercise prices assuming that the underlying stock does not go ex-dividend before the expiration of the options. If the underlying asset has a dividend of x, then the settled value of the box will be 10+x. Under the no-arbitrage assumption, the net premium paid out to acquire this position should be equal to the present value of the payoff. They are often called "alligator spreads" because the commissions “eat up” all your profit due to the large number of trades required for most box spreads. The box-spread usually combines two pairs of options; its name derives from the fact that the prices for these options form a rectangular box in two columns of a quotation. A similar trading strategy specific to futures trading is also known as a box or double butterfly spread.
Background
An arbitrage operation may be represented as a sequence which begins with zero balance in an account, initiates transactions at time t = 0, and unwinds transactions at time t = T so that all that remains at the end is a balance whose value B will be known for certain at the beginning of the sequence. If there were no transaction costs then a non-zero value for B would allow an arbitrageur to profit by following the sequence either as it stands if the present value of B is positive, or with all transactions reversed if the present value of B is negative. However, market forces tend to close any arbitrage windows which might open; hence the present value of B is usually insufficiently different from zero for transaction costs to be covered. This is considered typically to be a "Market Maker/ Floor trader" strategy only, due to extreme commission costs of the multiple-leg spread. If the box is for example 20 dollars as per lower example getting short the box anything under 20 is profit and long anything over, has hedged all risk. A present value of zero for B leads to a parity relation. Two well-known parity relations are:-
Spot futures parity. The current price of a stock equals the current price of a futures contract discounted by the time remaining until settlement:
Put call parity. A long European call c together with a short European put p at the same strike price K is equivalent to borrowing and buying the stock at price S. In other words, we can combine options with cash to construct a synthetic stock:
Note that directly exploiting deviations from either of these two parity relations involves purchasing or selling the underlying stock.
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 :
Long bull call-spread
Long bear put-spread
Long synthetic stock
Buy call at
Sell put at
Short synthetic stock
Sell call at
Buy put at
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-spread by reading the table diagonally. A long box-spread can be viewed as a long strangle at one pair of strike prices, and, plus a short strangle at the same pair of strike prices.
The long strangle contains the two long options.
The short strangle contains the two short options.
A short box-spread can be treated similarly.
An example
As an example, consider a three-month option on a stock whose current price is $100. If the interest rate is 8% per annum and the volatility is 30% per annum, then the prices for the options might be:
The initial investment for a long box-spread would be $19.30. The following table displays the payoffs of the 4 options for the three ranges of values for the terminal stock price :
The terminal payoff has a value of $20 independent of the terminal value of the share price. The discounted value of the payoff is $19.60. Hence there is a nominal profit of 40 cents to be had by investing in the long box-spread.
Prevalence
Surveys done by Chaput and Ederington on the Chicago Mercantile Exchange's market for options on Eurodollar futures showed between 1999 and 2000 some 25% of the trading volume was in outright options, 25% in straddles and vertical spreads, and about 5% in strangles. Guts constituted only about 0.1%, and box-spreads even less. Ratio spreads took more than 15%, and about a dozen other instruments took the remaining 30%. This is considered typically to be a "Market Maker/Floor trader" strategy only due to extreme commission costs of the multiple leg spread. In 2019, the online-only brokerage Robinhood changed its risk management policy due to a box spread suffering assignment risk from Reddit user 1R0NYMAN.
