Financial Management of Risks 445Written call options can also be used to hedge in certain circumstances.
Consider oil exporting nations such as Mexico and Venezuela. When oil prices
are low they are hungry for funds, funds that are much needed for national
development projects. When oil prices are high, they have plenty of excess
revenue. A reasonable strategy would be to sell high strike price oil call op-
tions when oil prices are low. The country thus receives premiums when
funds are most needed, and incurs a liability that only needs to be paid when
funds are most plentiful. The oil call options help to smooth the f low of funds
into the country. Abken and Feinstein (1994) elaborate on the use of written
call options in such a setting.
Warrants
Warrants are call options that are sold by the company whose stock is the under-
lying asset. If Microsoft pays its executive with Microsoft call options, those op-
tions will be called warrants. When the warrants are exercised, the total
outstanding supply of Microsoft stock will rise. Warrants are valuable, even if
they are not yet in the money. Clearly they must be worth something, other wise
executives would not want them and would give them away! Offering warrants as
compensation to executives is not free for the firm’s shareholders. Stories abound
nowadays of young Internet executives who became fabulously wealthy when
they exercised warrants paid to them as part of their employment compensation.
Put Options
The second type of option is a put. A put option is a contract that gives the
owner the right but not the obligation to sellsome underlying asset for a pre-
specified price, on or up to a given date. Consider a put option on Microsoft
stock. Suppose the strike price is $100 and the expiration date is December
15th. The put option owner has the right, but not the obligation to sell a share
of Microsoft stock for $100, on or up to December 15. If the market price of
Microsoft is above $100, for example $120, the put option owner would not ex-
ercise. Why should he force someone to pay $100 for the stock? He can make
more money by selling the stock in the open market. Thus, a put option is out
of the money if the stock price is abovethe strike price. If the stock price is
below the strike price, however, then the put option is in the money. If the
market price of Microsoft is $80 on December 15, the owner of the put can
reap a $20 payoff. To realize this payoff, he would buy the Microsoft stock in
the marketplace for $80, and then turn around and sell it for $100 by exercis-
ing his put option. Thus, a put option is in the money when the stock price is
below the strike price. A put option’s payoff at expiration, and its intrinsic
value prior to expiration, is the strike price minus the stock price, or zero,
whichever is greater.
Exhibit 13.3 presents the payoff diagram for a put option. Should the
stock price fall to zero, the put option’s payoff would be equal to the strike