Aside from the risks associated with early exercise implications, this
position is just about totally flat. The near-1.00 delta on the long synthetic
stock struck at 60 is offset by the near-negative-1.00 delta of the short
synthetic struck at 70. The tiny gammas and thetas of both combos are
brought closer to zero when they are spread against each another. Vega is
zero. And the bullish interest rate sensitivity of the long combo is nearly all
offset by the bearish interest sensitivity of the short combo. The stock can
move, time can pass, volatility and interest can change, and there will be
very little effect on the trader’s P&(L). The question is: Why would
someone trade a box?
Market makers accumulate positions in the process of buying bids and
selling offers. But they want to eliminate risk. Ideally, they try to be flat the
strike —meaning have an equal number of calls and puts at each strike
price, whether through a conversion or a reversal. Often, they have a
conversion at one strike and a reversal at another. The stock positions for
these cancel each other out and the trader is left with only the four option
legs—that is, a box. They can eliminate pin risk on both strikes by trading
the box as a single trade to close all four legs. Another reason for trading a
box has to do with capital.
Borrowing and Lending Money
The first thing to consider is how this spread is priced. Let’s look at another
example of a box, the October 50–60 box.
Long 1 October 60 call
Short 1 October 60 put
Short 1 October 70 call
Long 1 October 70 put