444 Planning and Forecasting
input variables. The formula is known as the Black-Scholes option pricing for-
mula. It is widely available on programmed computer software and in many
option theory textbooks.
A Written Call Option
In the case of life insurance or automobile insurance, when the insured party
collects another party must pay. It is a zero sum game. So it is with options. The
party that sells the option is liable for the future payoff. “ Writing” an option,
and “shorting” an option are synonymous with selling an option. The payoff di-
agram for a written call option position is the mirror image of the long or
bought call option position. As shown in Exhibit 13.2, the x-axis is the ref lect-
ing surface.
Note that once the call option writer has received the initial premium, all
subsequent cash f lows will be outf lows. The best the writer can hope for is that
the call will expire out of the money. Note that the potential liability of the
written option position is unlimited. Notice as well, that the amount of money
the buyer of the option might receive at expiration is the exact amount that
writer will have to pay. Thus, when the media report that a particular company
has lost millions of dollars in options, the reader should realize that this means
some other party has made millions. The newspapers tend to focus on the
losers.
Strategies Using Written Call Options
Why would anybody wish to sell a call option if doing so subjects them to the
possibility of unlimited future liabilities? One answer is that speculators some-
times deem the risks worthwhile in light of the expected reward. They may be
confident that the underlying asset price will not rise and the option will ex-
pire worthless.
EXHIBIT 13.2 Payoff diagram for a written call option position.
–30–10
–2001020300 10203040506070 80 90100Payoff (dollars)Terminal stock price (Strike price = $70)