EXHIBIT 13.4 The effect of time on P&(L).
As time passes, the reduction in profit is reflected by the center point of
the graph dipping farther into negative territory. That is the effect of time
decay. The long options will have lost value at that future date with the
stock still at the same price (all other factors held constant). Still, a move in
either direction can lead to a profitable position. Ultimately, at expiration,
the payoff takes on a rigid kinked shape.
In the delta-neutral long call examples used in this chapter the position
becomes net long stock if the calls are in-the-money at expiration or net
short stock if they are out-of-the-money and only the short stock remains.
Volatility, as well, would move the payoff line vertically. As IV increases,
the options become worth more at each stock price, and as IV falls, they are
worth less, assuming all other factors are held constant.
A delta-neutral short-gamma play would have a P&(L) diagram quite the
opposite of the smiley-faced long-gamma graph. Exhibit 13.5 shows what is
called the short-gamma frown.