be exercised? Will the puts get assigned? If the puts are assigned, the
traders are left with no short stock and should let the calls expire without
exercising so as not to have a long delta position after expiration. If the puts
are not assigned, they should exercise the calls to get delta flat. It’s also
possible that only some of the puts will be assigned.
Because they don’t know how many, if any, of the puts will be assigned,
the market makers have pin risk. To avoid pin risk, market makers try to
eliminate their position if they have conversions or reversals close to
expiration.
Boxes and Jelly Rolls
There are two other uses of synthetic stock positions that form conventional
strategies: boxes and rolls.
Boxes
When long synthetic stock is combined with short synthetic stock on the
same underlying within the same expiration cycle but with a different strike
price, the resulting position is known as a box. With a box, a trader is
synthetically both long and short the stock. The two positions, for all intents
and purposes, offset each other directionally. The risk of stock-price
movement is almost entirely avoided. A study of the greeks shows that the
delta is close to zero. Gamma, theta, vega, and rho are also negligible.
Here’s an example of a 60–70 box for April options:
Short 1 April 60 call
Long 1 April 60 put
Long 1 April 70 call
Short 1 April 70 put
In this example, the trader is synthetically short the 60-strike and, at the
same time, synthetically long the 70-strike. Exhibit 6.9 shows the greeks.
EXHIBIT 6.9 Box greeks.