Suppose you're an investor and are curious what the market thinks the implied volatility of the S&P 500 is today. You know a few things:
- You can assume that every other investor is using Black-Scholes-Merton formula for pricing.
- You look a common ETF of the S&P 500, the SPY spider.
- Today it's priced at $216.
- A European call option has a strike price of $210.
- To expire, there are 30 days left from today.
- The risk-free interest rate is 1.8%.
- The market is pricing this European call option at $7.93.
What is the implied volatility?
(All answers are truncated.)
Note: Using Excel's "Goal Seek" may be helpful.