2-Financial Markets Page 66 Wednesday, February 4, 2004 1:15 PM
66 The Mathematics of Financial Modeling and Investment ManagementRisk-Return for Options
The maximum amount that an option buyer can lose is the option price.
The maximum profit that the option writer can realize is the option
price. The option buyer has substantial upside return potential, while
the option writer has substantial downside risk.
Notice that, unlike in a futures contract, one party to an option con-
tract is not obligated to transact—specifically, the option buyer has the
right but not the obligation to transact. The option writer does have the
obligation to perform. In the case of a futures contract, both buyer and
seller are obligated to perform. Of course, a futures buyer does not pay
the seller to accept the obligation, while an option buyer pays the seller
an option price.
Consequently, the risk/reward characteristics of the two contracts are
also different. In the case of a futures contract, the buyer of the contract
realizes a dollar-for-dollar gain when the price of the futures contract
increases and suffers a dollar-for-dollar loss when the price of the futures
contract drops. The opposite occurs for the seller of a futures contract.
Options do not provide this symmetric risk/reward relationship. The most
that the buyer of an option can lose is the option price. While the buyer of
an option retains all the potential benefits, the gain is always reduced by the
amount of the option price. The maximum profit that the writer may real-
ize is the option price; this is offset against substantial downside risk. This
difference is extremely important because investors can use futures to pro-
tect against symmetric risk and options to protect against asymmetric risk.The Option Price
Determining the value of an option is not as simple as the value of a
futures contract. In Chapter 15 we will present a model employing sto-
chastic calculus and arbitrage arguments to determine the theoretical
price of an option. In this section we simply present the factors that
affect the valuation of an option.Basic Components of the Option Price
The option price is a reflection of the option’s intrinsic value and any
additional amount over its intrinsic value. The premium over intrinsic
value is often referred to as the time premium.
The intrinsic value of an option is the economic value of the option
if it is exercised immediately, except that if there is no positive economic
value that will result from exercising immediately then the intrinsic
value is zero. The intrinsic value of a call option is the difference
between the current price of the underlying asset and the strike price if
positive; it is otherwise zero. For example, if the strike price for a call