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Here is an actual example. At the end of September 2001, common stock in network hardware manufacturer Cisco was trading for $12.18. A call option expiring in January 2002 with a strike price of $12.50 traded for $1.75. Treasury bills maturing in late January were paying 2.35 percent. Based on this information, how volatile is the return on Cisco predicted to be?

Just to summarize, the relevant numbers we have are:

From here, it's plug and chug. As you have probably figured out by now, it's easier to use an options calculator to solve this problem. That's what we did; the implied standard deviation is about 66 percent. Our nearby Work the Web box shows you how to do this.

In principle, to solve this problem, we need to convert the interest rate of 2.35 percent to a continuously compounded rate. If we do, we get 2.323 percent. However, we've seen that option values are not very sensitive to small changes in interest rates, and, in this case, it actually makes almost no difference. For this reason, in practice, the continuous compounding issue is often ignored, particularly when rates are low.

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