A4-1
1
APPENDIX 4
OPTION PRICING
In general, the value of any asset is the present value of the expected cash flows
on that asset. In this appendix, we will consider an exception to that rule when we will
look at assets with two specific characteristics:
•
They derive their value from the values of other assets.
•
The cash flows on the assets are contingent on the occurrence of specific events.
These assets are called options, and the present value of the expected cash flows on them
will understate their true value. We will describe the cash flow characteristics of options,
consider the factors that determine their value, and examine how best to value them.
Cash Flows on Options
There are two types of options. A
call option
gives the buyer of the option the right
to buy the underlying asset at a fixed price, whereas a
put option
gives the buyer the right
to sell the underlying asset at a fixed price. In both cases, the fixed price at which the
underlying asset can be bought or sold is called the
strike
or
exercise price
.
To look at the payoffs on an option, consider first the case of a call option. When
you acquire the right to buy an asset at a fixed price, you want the price of the asset to
increase above that fixed price. If it does, you make a profit, because you can buy at the
fixed price and then sell at the much higher price; this profit has to be netted against the
cost initially paid for the option. However, if the price of the asset decreases below the
strike price, it does not make sense to exercise your right to buy it at a higher price. In
this scenario, you lose what you originally paid for the option. Figure A4.1 summarizes
the cash payoff at expiration to the buyer of a call option.
A4-2
2
With a put option, you get the right to sell at a fixed price, and you want the price
of the asset to decrease below the exercise price. If it does, you buy the asset at the
current price and then sell it back at the exercise
price, claiming the difference as a gross
profit. When the initial cost of buying the option is netted against the gross profit, you
arrive at an estimate of the net profit. If the value of the asset rises above the exercise
price, you will not exercise the right to sell at a lower price. Instead, the option will be
allowed to expire without being exercised, resulting in a net loss of the original price paid
for the put option. Figure A4.2 summarizes the net payoff on buying a put option.
With both call and put options, the potential for profit to the buyer is significant, but the
potential for loss is limited to the price paid for the option.