Implied Volatility (IV)
Implied volatility is the market's expectation of future price movement, expressed as an annualized percentage.
IV is the volatility number that makes the model price match the market price.
Key Points
- IV is forward-looking - what the market expects, not what happened
- IV is not direction - it measures magnitude of expected moves, not up or down
- Higher IV → higher option prices (all else equal)
What IV Actually Tells You
IV translates directly to an expected price range. If BTC is at $100,000 with 50% IV, the market expects BTC to stay within ±$50,000 over a year (1 standard deviation = 68% probability).
For shorter timeframes, the expected move shrinks by √time - a 30-day move is much smaller than a 365-day move.
How It Works
IV is "implied" because we work backwards:
- See the market price of an option
- Plug in spot, strike, time, and rates into Black-Scholes
- Solve for the volatility that produces that price
IV vs Historical Volatility
| Implied Volatility (IV) | Historical Volatility (HV) |
|---|---|
| Forward-looking | Backward-looking |
| Derived from option prices | Calculated from past returns |
| What the market expects | What actually happened |
When IV > HV: Market expects more volatility than recently observed When IV < HV: Market expects calmer conditions
Why IV Matters
Options Get Expensive When IV Is High
| High IV | Low IV |
|---|---|
| Market expects large moves | Market expects small moves |
| Options are expensive | Options are cheap |
| Sellers get more premium | Buyers pay less |
You Can Be Right and Still Lose
If you buy a call expecting BTC to rise:
- BTC rises 3%
- But IV drops from 80% to 50% ("vol crush")
- Your call loses value despite being right on direction
This is vega risk.
When IV Changes
IV increases when:
- Major events approach (FOMC, protocol upgrades)
- Uncertainty rises
- Large unexpected moves occur
IV decreases when:
- Events pass ("vol crush")
- Markets become range-bound
- Uncertainty resolves
Typical IV Levels
| Asset | Typical IV Range |
|---|---|
| BTC options | 40–100%+ |
| ETH options | 50–120%+ |
| SPX options | 10–30% |
Crypto IV is higher because crypto is more volatile.
Building mathematical intuition
Learn implied volatility from scratchInteractive lesson · no prerequisitesThe interactive lesson covers what implied volatility is (the σ that makes Black-Scholes match the market price), how IV is solved via root-finding inversion, why IV matters as the market's consensus on future uncertainty, how IV varies by strike (the volatility smile and skew), and how to convert IV into expected daily, weekly, and monthly price ranges.
Open source implementations
| Repo | Why inspect it |
|---|---|
| lets_be_rational | State-of-the-art IV solver (Jackel's method) |
| py_vollib | Bisection and Newton IV solvers in Python |
| QuantLib | Multiple IV solver backends |
Related:
- Types of Options Trades - How each trade structure interacts with IV
- Vega - Sensitivity to IV changes
- Option Valuation - How IV affects extrinsic value
- Lesson 5: Implied Volatility - Full explainer