Ross et al.: Fundamentals
of Corporate Finance, Sixth
Edition, Alternate EditionVIII. Topics in Corporate
Finance(^844) 24. Option Valuation © The McGraw−Hill
Companies, 2002
effect varies depending on the “moneyness” of the option (i.e., how far in or out of the
money it is).
For a given set of input values, we illustrate the relationship between call and put op-
tion prices and the underlying stock price in Figure 24.1. In the figure, stock prices are
measured on the horizontal axis and option prices are measured on the vertical axis. No-
tice that the lines for put and call values are bowed. The reason is that the value of an
option that is far out of the money is not as sensitive to a change in the underlying stock
price as an in-the-money option.
The sensitivity of an option’s value to small changes in the price of the underlying
stock is called the option’s delta. For European options, we can directly measure the
deltas as follows:
CHAPTER 24 Option Valuation 819
The Black-Scholes OPMis a wonderful tool, but as we have seen, the
calculations can get somewhat tedious. One way to find the price of an
option without the effort is to work the Web. We went to the options calcu-
lator at the Chicago Board Options Exchange, http://www.cboe.com. Suppose we
have an option with a strike price of $75 that expires in October. The current stock
price is $72.62, the standard deviation of the stock’s return is 48 percent per year,
and the risk-free rate is 3.2 percent. Assuming the stock does not pay dividends, this
is what we get:
As you can see, a call option on this stock should sell for about $3.28 and a put op-
tion should sell for $5.46. Now that’s easy! Notice that the “greeks” are also calcu-
lated. What does “gamma” tell you? Visit the web site to learn more.
Work the Web
Another good options
calculator can be found at
http://www.numa.com.
delta
Measures the effect on
an option’s value of a
small change in the value
of the underlying stock.