Option prices are determined in part by volatility, and traders sometimes use the volatility estimates built into option prices to assess market conditions. The volatility estimate built into S&P 500 options may be found at Yahoo! Finance (get quotes for ticker symbol VIX). If you look at the historical plot of the VIX index, you'll see that it spikes during periods of turbulence (e.g., the recent subprime crisis or the lead-up to the invasion of Iraq), and for this reason it is often called a "fear gauge." Let's see how traders back out these estimates of

Volatility from option prices to do so, consider the option in Challenge Problem 29. Assume that option traders see the option selling at a price of $9.50 and wonder what volatility level this price implies.
a. Go to the Tools menu of the Black-Scholes spreadsheet in this chapter (available at our Web site, www.mhhe.com/bmm7e), look under the Data tab for What-If Analysis, select Goal Seek, and a dialog box will appear. Use the dialog box to "set cell E7 to value 9.50 by changing cell B2." This directs the spreadsheet to change the value of cell B2 (the volatility estimate) to a level that makes the option price (cell E7) equal to $9.50. The resulting volatility parameter is called the option's implied volatility, that is, the volatility level implied by its market price. This sort of inference is the basis for the VIX index.
b. What happens to implied volatility if the option price is only $9? Why has it decreased?

$30 S430 $460 $490 Stock price