Two Kinds of Volatility

Historical volatility (HV) — also called realized or statistical volatility — measures how much a stock actually moved over a past period. It's a backward-looking, factual number calculated from closing prices.

Implied volatility (IV) measures how much the options market expects a stock to move going forward. It's a forward-looking estimate derived from option prices.

Think of it this way: HV is the weather report for last week. IV is the forecast for next week.

How Historical Volatility Is Calculated

HV is the annualized standard deviation of daily log returns over a chosen lookback period (commonly 20, 30, or 60 trading days).

Simplified steps:

  • Calculate daily percentage changes in closing price
  • Find the standard deviation of those changes
  • Annualize by multiplying by √252

    • Example: If a stock's daily returns over 20 days have a standard deviation of 1.5%, then:

  • 20-day HV = 1.5% × √252 = 23.8%

    • This means the stock has been moving at a pace consistent with about 24% annualized volatility.

    How Implied Volatility Is Derived

    IV isn't calculated from historical data. It's extracted from option prices. By plugging a market-traded option price into the Black-Scholes model alongside known inputs (stock price, strike, time, rates), you solve for the volatility that produces that price.

    If a $100 call expiring in 30 days trades at $4.50, the Black-Scholes model might require a volatility input of 32% to produce that $4.50 theoretical price. That 32% is the implied volatility.

    The Volatility Risk Premium: IV > HV (Most of the Time)

    Here's the most important relationship in options trading: implied volatility is almost always higher than subsequently realized volatility. This gap is called the volatility risk premium (VRP).

    Why it exists: Option buyers are willing to pay a premium above fair value because options provide insurance against large moves. Sellers demand compensation for the tail risk they absorb. The result is that option premiums embed a consistent markup.

    Across a long-term study of SPX options, IV overestimated realized volatility roughly 85% of the time. The average overstatement was about 3-4 percentage points.

    This volatility risk premium is the structural foundation of every premium-selling strategy. When you sell options, you're harvesting this premium over time.

    When IV < HV: The Warning Sign

    Occasionally, implied volatility drops below historical volatility. This means the market is pricing in less future movement than the stock has actually been exhibiting. This is unusual and often signals:

  • Complacency before a catalyst — the market hasn't priced in an upcoming event
  • A potential buying opportunity — options are genuinely cheap
  • An anomaly — sometimes illiquid options misprice

    • When you spot IV significantly below HV, it's worth investigating whether there's a catalyst that the market is underpricing.

    Practical Comparison Framework

    | Metric | Historical Volatility | Implied Volatility | DirectionBackward-lookingForward-looking SourceStock price dataOption prices What it tells youHow much the stock movedHow much the market expects it to move Use caseBenchmark for "normal" movementDetermines if options are cheap or expensive | Affected by | Past price moves | Supply/demand for options, events |

    Using the HV-IV Relationship in Trading

    IV much higher than HV (IV/HV ratio > 1.3): Options are expensive relative to recent movement. Favor selling strategies — the premium you collect is likely more than what gets realized.

    IV near HV (ratio between 0.9-1.1): Options are fairly priced. No particular edge for buyers or sellers. Trade based on directional conviction rather than volatility.

    IV below HV (ratio < 0.9): Options are cheap. Consider buying strategies — debit spreads, long straddles, or protective puts. You're getting a discount on expected movement.

    OptionsPilot surfaces both implied and historical volatility data when analyzing specific stocks, helping you gauge whether options premiums offer good value relative to actual stock movement.

    Key Takeaway

    Never trade options without checking both HV and IV. The relationship between them tells you whether premiums are rich, fair, or cheap — and that single data point should influence every strategy choice you make.