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+EXHIBIT 9.13 Isabel’s long put spread in Johnson & Johnson.
+62.50–65 Put Spread
+Delta −0.273
+Gamma−0.001
+Theta +0.005
+Vega −0.006
+These two spreads were bought for a combined total of 2.50. The
+collective position, composed of the four legs of these two spreads, forms a
+new strategy altogether.
+The two traders together have created a box. This box, which is empty of
+both profit and loss, is represented by greeks that almost entirely offset each
+other. Sam’s positive delta of 0.29 is mostly offset by Isabel’s −0.273 delta.
+Gamma, theta, and vega will mostly offset each other, too.
+Chapter 6 described a box as long synthetic stock combined with short
+synthetic stock having a different strike price but the same expiration
+month. It can also be defined, however, as two vertical spreads: a bull (bear)
+call spread plus a bear (bull) put spread with the same strike prices and
+expiration month.
+The value of a box equals the present value of the distance between the
+two strike prices (American-option models will also account for early
+exercise potential in the box’s value). This 2.50 box, with 38 days until
+expiration at a 1 percent interest rate, has less than a penny of interest
+affecting its value. Boxes with more time until expiration will have a higher
+interest rate component. If there was one year until expiration, the
+combined value of the two verticals would equal 2.475. This is simply the
+distance between the strikes minus interest (2.50–[2.50 × 0.01]).
+Credit spreads are often made up of OTM options. Traders betting against
+a stock rising through a certain price tend to sell OTM call spreads. For a
+stock at $50 per share, they might sell the 55 calls and buy the 60 calls. But
+because of the synthetic relationship that verticals have with one another,
+the traders could buy an ITM put spread for the same exposure, after