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, you'll see that it spikes during periods of turbulence (e.g., the subprime crisis in 2008 or the lead-up to the Brexit vote in June 2016), 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 the previous problem. 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 Black-Scholes spreadsheet in this chapter (available in Connect) and go to the sheet Implied Volatility. In the box on the right, enter the value of $9.50. Press Find Std Dev and you will see 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.
b. What happens to implied volatility if you enter a lower call value? Why has it decreased?