Here we'll use the bisection method introduced in Chapter 3, Financial Mathematics and Numerical Analysis. This is a numerical method for finding roots. The implied volatility is the root where the function value is zero for the Black-Scholes function for different input parameters. The volatility of an underlying instrument is the input to Black-Scholes which gives the same price as the current price of the option.
Vega tells us about the sensitivity in the option price for the changes in the volatility of the underlying asset. Look at Yahoo! Finance and find the option data. Take that option data into the following solve function:
Figure 2: The VIX-index for the S&P500 index options from 2000-01-01 to 2013-11-01
The VIX-index, as seen in the preceding screenshot, is an index which combines the implied volatility of S&P 500 index options. This can be interpreted as an indication of future volatility.