Day Three
On this day, the market trends. First, the stock rises $0.50, at which point
Harry sells 140 shares of stock at $40.50 to lock in gains from his delta and
to get flat. However, the market continues to rally. At $41 a share, Harry is
long another 1.40 deltas and so sells another 140 shares. The rally
continues, and at $41.50 he sells another 140 shares to cover the delta.
Finally, at the end of the day, the stock closes at $42 a share. Harry sells a
final 140 shares to get flat.
There was not any literal scalping of stock today. It was all selling.
Nonetheless, gamma trading led to a profitable day.
As the stock rose from $40 to $40.50, 140 deltas were created from
positive gamma. Because the delta was zero at $40 and 140 at $40.50, the
estimated average delta is found by dividing 140 in half. This estimated
average delta multiplied by the $0.50 gain on the stock equals a $35 profit.
The delta was zero after the adjustment made at $40.50, when 140 shares
were sold. When the stock reached $41, another $35 was reaped from the
average delta of 70 over the $0.50 move. This process was repeated every
time the stock rose $0.50 and the delta was covered.