Box spread
Encyclopedia
In options
trading, a box spread is a combination of positions that has a certain (i.e. riskless) payoff, considered to be simply "delta neutral interest rate position". For example, a bull spread
constructed from calls (e.g. long a 50 call, short a 60 call) combined with a bear spread
constructed from puts (e.g. long a 60 put, short a 50 put), has a constant payoff of the difference in exercise prices (e.g. 10). 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; and its name derives from the fact that the prices for these options form a rectangular box in two columns of a quotation.
Note that box spreads also form a strategy in futures trading - see below.
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:-
Note that directly exploiting deviations from either of these two parity relations involves purchasing or selling the underlying stock.
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. [Normally, the discounted payoff would differ little from the net premium, and any nominal profit would be consumed by transaction costs.]
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 (assume strike-prices
< 
):-
Reading the table horizontally and vertically we obtain two views of a long box-spread.
We can obtain a third view of the long box-option by reading the table diagonally. In order to interpret the diagonals we need to introduce the straddle, which is a combination of a long call and a long put both at a strike price equal to the current stock price (at-the-money). This combination is direction neutral, its terminal payoff being dependent not on the direction of movement of the stock price but only on the magnitude of the movement. The band between the break-even points can be extended by separating the strike prices of the two options symmetrically with respect to the current stock price:-
Returning to the long box-spread, we see that the leading diagonal is a long gut combination, and the other diagonal is a short strangle combination. Hence a long box-spread may be created as a coupling of a long gut with a short strangle.
The short box-spread can be treated similarly.
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 30 cents to be had by investing in the long box-spread.
's market for options on Eurodollar
futures
. For the year 1999-2000 they found that some 25% of the trading volume was in outright options, 25% in straddles and vertical spreads (call-spreads and put-spreads), and about 5% in strangles. Guts constituted only about 0.1%, and box-spreads even less (about 0.01%). [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. 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.]
For linear commodities instruments (ie, futures, forwards, swaps), "box spread" is used to refer to a four-leg position consisting of long a two-leg spread in one time period, and short the same two-leg spread in another time period. For instance, "buying the Cal 13-12, SP-NP box spread", would be buying power at CAISO hub SP-15 versus selling power at CAISO hub NP-15 for 2013, while also doing the opposite (so, selling at SP-15 and buying at NP-15) for 2012. (Customarily, a leg that is purchased is mentioned before a leg that is sold. And commonly, the more expensive leg is also mentioned first (to avoid using a negative spread price). Therefore, the way that the CAISO box spread is referred to suggests that SP is trading over NP, and SP-minus-NP is wider in 2013 than in 2012.) One motivation for trading a box would be to roll an existing two-leg spread position to another (typically later) time period. Eg, to roll one's existing 2012 SP-NP spread position out to 2013 (ie, close 2012 and replace with 2013). Another motivation would be to trade the box position itself, taking a view that there will be a trend for a two-leg spread (widening or narrowing) over time.
Option (finance)
In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...
trading, a box spread is a combination of positions that has a certain (i.e. riskless) payoff, considered to be simply "delta neutral interest rate position". For example, a bull spread
Bull spread
In options trading, a bull spread is a bullish, vertical spread options strategy that is designed to profit from a moderate rise in the price of the underlying security....
constructed from calls (e.g. long a 50 call, short a 60 call) combined with a bear spread
Bear spread
In options trading, a bear spread is a bearish, vertical spread options strategy that can be used when the options trader is moderately bearish on the underlying security....
constructed from puts (e.g. long a 60 put, short a 50 put), has a constant payoff of the difference in exercise prices (e.g. 10). Under the no-arbitrage
No-arbitrage bounds
In financial mathematics, no-arbitrage bounds are mathematical relationships specifying limits on financial portfolio prices. These price bounds are a specific example of good-deal bounds, and are in fact the greatest extremes for good-deal bounds....
assumption the net premium paid out to acquire this position should be equal to the present value
Present value
Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...
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; and its name derives from the fact that the prices for these options form a rectangular box in two columns of a quotation.
Note that box spreads also form a strategy in futures trading - see below.
Background
An arbitrageArbitrage
In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...
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
Present value
Present value, also known as present discounted value, is the value on a given date of a future payment or series of future payments, discounted to reflect the time value of money and other factors such as investment risk...
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.
The Box Spread
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. [Normally, the discounted payoff would differ little from the net premium, and any nominal profit would be consumed by transaction costs.]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 (assume strike-prices
< ):-| 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-option by reading the table diagonally. In order to interpret the diagonals we need to introduce the straddle, which is a combination of a long call and a long put both at a strike price equal to the current stock price (at-the-money). This combination is direction neutral, its terminal payoff being dependent not on the direction of movement of the stock price but only on the magnitude of the movement. The band between the break-even points can be extended by separating the strike prices of the two options symmetrically with respect to the current stock price:-
- If both options are in-the-money the combination is called a long gut.
- If both options out-of-the-money the combination is called a long strangle.
Returning to the long box-spread, we see that the leading diagonal is a long gut combination, and the other diagonal is a short strangle combination. Hence a long box-spread may be created as a coupling of a long gut with a short strangle.
The 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% pa and the volatility is 30% pa then the prices for the options might be:| Call | Put | |
|---|---|---|
 |
$13.10 | $ 1.65 |
 |
$ 3.05 | $ 10.90 |
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 30 cents to be had by investing in the long box-spread.
Prevalence
To what extent are the various instruments introduced above traded on exchanges? Chaput and Ederington, surveyed Chicago Mercantile ExchangeChicago Mercantile Exchange
The Chicago Mercantile Exchange is an American financial and commodity derivative exchange based in Chicago. The CME was founded in 1898 as the Chicago Butter and Egg Board. Originally, the exchange was a non-profit organization...
's market for options on Eurodollar
Eurodollar
Eurodollars are time deposits denominated in U.S. dollars at banks outside the United States, and thus are not under the jurisdiction of the Federal Reserve. Consequently, such deposits are subject to much less regulation than similar deposits within the U.S., allowing for higher margins. The term...
futures
Futures contract
In finance, a futures contract is a standardized contract between two parties to exchange a specified asset of standardized quantity and quality for a price agreed today with delivery occurring at a specified future date, the delivery date. The contracts are traded on a futures exchange...
. For the year 1999-2000 they found that some 25% of the trading volume was in outright options, 25% in straddles and vertical spreads (call-spreads and put-spreads), and about 5% in strangles. Guts constituted only about 0.1%, and box-spreads even less (about 0.01%). [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. 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.]
The box spread in futures
A box spread in futures contracts is a spread from two consecutive butterfly spreads, summing to +1 -3 +3 -1 in consecutive, or at least equally spaced, contracts. Often presumed not to move much (as in theory they are practically non directional) and therefore trade in a range.For linear commodities instruments (ie, futures, forwards, swaps), "box spread" is used to refer to a four-leg position consisting of long a two-leg spread in one time period, and short the same two-leg spread in another time period. For instance, "buying the Cal 13-12, SP-NP box spread", would be buying power at CAISO hub SP-15 versus selling power at CAISO hub NP-15 for 2013, while also doing the opposite (so, selling at SP-15 and buying at NP-15) for 2012. (Customarily, a leg that is purchased is mentioned before a leg that is sold. And commonly, the more expensive leg is also mentioned first (to avoid using a negative spread price). Therefore, the way that the CAISO box spread is referred to suggests that SP is trading over NP, and SP-minus-NP is wider in 2013 than in 2012.) One motivation for trading a box would be to roll an existing two-leg spread position to another (typically later) time period. Eg, to roll one's existing 2012 SP-NP spread position out to 2013 (ie, close 2012 and replace with 2013). Another motivation would be to trade the box position itself, taking a view that there will be a trend for a two-leg spread (widening or narrowing) over time.