Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionVIII. Topics in Corporate
Finance- Risk Management: An
Introduction to Financial
Engineering
© The McGraw−Hill^823
Companies, 2002Options versus Forwards
There are two key differences between an option contract and a forward contract. The
first is obvious. With a forward contract, both parties are obligated to transact; one party
delivers the asset, and the other party pays for it. With an option, the transaction occurs
only if the owner of the option chooses to exercise it.
The second difference between an option and a forward contract is that, whereas no
money changes hands when a forward contract is created, the buyer of an option con-
tract gains a valuable right and must pay the seller for that right. The price of the option
is frequently called the option premium.
Option Payoff Profiles
Figure 23.11 shows the general payoff profile for a call option from the owner’s view-
point. The horizontal axis shows the difference between the asset’s value and the strike
price on the option. As illustrated, if the price of the underlying asset rises above the
strike price, then the owner of the option will exercise the option and enjoy a profit. If
the value of the asset falls below the strike price, the owner of the option will not exer-
cise it. Notice that this payoff profile does not consider the premium that the buyer paid
for the option.
The payoff profile that results from buying a call is repeated in Part A of Figure
23.12. Part B shows the payoff profile on a call option from the seller’s side. A call op-
tion is a zero-sum game, so the seller’s payoff profile is exactly the opposite of the
buyer’s.
Part C of Figure 23.12 shows the payoff profile for the buyer of a put option. In this
case, if the asset’s value falls below the strike price, then the buyer profits because the
seller of the put must pay the strike price. Part D shows that the seller of the put option
loses out when the price falls below the strike price.
Option Hedging
Suppose a firm has a risk profile that looks like the one in Part A of Figure 23.13. If the
firm wishes to hedge against adverse price movements using options, what should it do?
Examining the different payoff profiles in Figure 23.12, we see that the one that has the
desirable shape is C, buying a put. If the firm buys a put, then its net exposure is as il-
lustrated in Part B of Figure 23.13.
In this case, by buying a put option, the firm has eliminated the downside risk, that
is, the risk of an adverse price movement. However, the firm has retained the upside po-
tential. In other words, the put option acts as a kind of insurance policy. Remember that
this desirable insurance is not free; the firm pays for it when it buys the put option.
Hedging Commodity Price Risk with Options
We saw earlier that there are futures contracts available for a variety of basic commodi-
ties. In addition, there are an increasing number of options available on these same com-
modities. In fact, the options that are typically traded on commodities are actually
options on futures contracts, and, for this reason, they are called futures options.
The way these work is as follows: When a futures call option on, for example, wheat
is exercised, the owner of the option receives two things. The first is a futures contract
on wheat at the current futures price. This contract can be immediately closed at no cost.
The second thing the owner of the option receives is the difference between the strike
price on the option and the current futures price. The difference is simply paid in cash.
CHAPTER 23 Risk Management: An Introduction to Financial Engineering 797The Chicago Board
Options Exchange (CBOE)
is the world’s largest
options exchange. Make
a virtual visit at
http://www.cboe.com.A good introduction to the
options markets is
available at
http://www.optionscentral.com.The Derivatives ’Zineat
http://www.margrabe.com
covers risk management.