But just looking at delta only tells a part of the story. In reality, the delta
does not remain constant during the price rise in Johnson & Johnson but
instead becomes more negative. Initially, the delta is −0.34 and the gamma
is −0.15. After a rise in the stock price, the delta will be more negative by
the amount of the gamma. To account for the entire effect of direction,
Brendan needs to take both delta and gamma into account. He needs to
estimate the average delta based on gamma during the stock price move.
The formula for the change in stock price is
Taking into account the effect of gamma as well as delta, Johnson &
Johnson needs to rise only $1.01, in order for Brendan’s calls to be offered
at his stop-loss price of 1.10.
While having a predefined price point to cover in the event the underlying
rises is important, sometimes traders need to think on their feet. If material
news is announced that changes the fundamental outlook for the stock,
Brendan will have to adjust his plan. If the news leads Brendan to become
bullish on the stock, he should exit the trade at once, taking a small loss
now instead of the bigger loss he would expect later. If the trader is
uncertain as to whether to hold or close the position, the Would I Do It
Now? rule is a useful rule of thumb.