Implied Volatility
Extracting the only unknown — and what the market is telling you when it changes
Five inputs go into the Black-Scholes formula. Four are observable: the stock's current price, the strike, the time to expiration, and the risk-free rate. Dividends, when present, are also observable.
One input is not: the stock's volatility going forward. Volatility is the missing number, and the market, by quoting an option price, is implicitly telling you what σ it considers most accurate. The standard practice — used on every option desk and in every pricing system in the world — is to take that quoted price, plug all four observable inputs into BSM, and solve backward for the σ that makes the formula match the market quote.
The resulting number is called implied volatility, and it is the most-watched single number in derivatives markets. Implied volatility is what professional traders mean when they say 'vol' in shorthand. It is what the VIX measures.
That is the opening. Finishing a lesson is where it stops being interesting and starts being useful: the full lesson runs to 7 sections and ends with 6 practice questions. A free account is what opens the rest, and the other 255 lessons in the Academy with it. No card.
What this lesson covers
- 1How implied volatility is actually computed
- 2IV percentile and IV rank — the two contextual measures that matter
- 3Newton-Raphson IV extraction in pseudocode
- 4VIX vs. subsequent SPX realized volatility — directional patterns
- 5VIX peak, March 16, 2020 — implied volatility's tail-event maximum
- 6Where to see this on the platform
- 7Summary