options to me at prices I wanted to buy them—my bid—and buying options
from me at prices I wanted to sell them—my offer. Upon making an option
trade, I needed to hedge directional risk immediately. I usually did so by
offsetting my option trades by taking the opposite delta position in the stock
—especially on big-delta trades. Through this process of providing liquidity
to the market, I built up option-centric risk.
To manage this risk I needed to watch my other greeks. To be sure, trying
to draw a P&L diagram of this position would be a fruitless endeavor.
Exhibit 16.8 shows the risk of this trade in its most distilled form.
EXHIBIT 16.8 Analytics for market-maker position in Ford Motor Co.
(stock at $15.72).
Delta +1,075
Gamma−10,191
Theta +1,708
Vega +7,171
Rho −33,137
The +1,075 delta shows comparatively small directional risk relative to
the −10,191 gamma. Much of the daily task of position management would
be to carefully guard against movement by delta hedging when necessary to
earn the $1,708 per day theta.
Much of the negative gamma/positive theta comes from the combined
1,006 short January 15 calls and puts. (Note that because this position is
traded delta neutral, the net long or short options at each strike is what
matters, not whether the options are calls or puts. Remember that in delta-
neutral trading, a put is a call, and a call is a put.) The positive vega stems
from the fact that the position is long 1,927 January 2003 20-strike options.
Although this position has a lot going on, it can be broken down many
ways. Having long LEAPS options and short front-month options gives this
position the feel of a time spread. One way to think of where most of the
gamma risk is coming from is to bear in mind that the 15 strike is
synthetically short 503 straddles (1,006 options ÷ two). But this position
overall is not like a straddle. There are more strikes involved—a lot more.
There is more short gamma to the downside if the price of Ford falls toward
$12.50. To the upside, the 17.50 strike is long a combined total of 439
options. Looking at just the 15 and 17.50 strikes, we can see something that