Defining the Two Volatilities

Realized volatility (RV) is what happened. It's the annualized standard deviation of actual daily returns over a specific lookback period. If you measure AAPL's daily returns over 20 trading days and annualize that standard deviation, you get the 20-day realized volatility.

Implied volatility (IV) is what the market expects to happen. It's extracted from current option prices. If AAPL's 30-day ATM options are priced at a level consistent with 28% annualized volatility, that's the implied volatility.

The gap between them — the volatility risk premium — is one of the most persistent tradeable phenomena in financial markets.

Calculating Realized Volatility

Step 1: Collect daily closing prices for N trading days (typically 20 or 30).

Step 2: Calculate daily log returns: ln(Close today / Close yesterday) for each day.

Step 3: Compute the standard deviation of these log returns.

Step 4: Annualize: multiply by √252 (trading days per year).

Example using 5 days of AAPL data:

| Day | Close | Daily Return | Mon$190.00— Tue$192.50+1.31% Wed$191.00-0.78% Thu$193.00+1.04% | Fri | $194.50 | +0.78% |

Standard deviation of returns: 0.89% Annualized RV: 0.89% × √252 = 14.1%

In practice, use 20-30 trading days for a meaningful sample.

The Volatility Risk Premium (VRP)

The VRP is simply: VRP = IV - RV

When IV is 28% and subsequent RV turns out to be 22%, the VRP was +6 percentage points. Option sellers who sold at 28% IV effectively collected 6% more than the actual movement justified.

Historical averages (SPX):

  • Mean IV: ~19-20%
  • Mean RV: ~15-16%
  • Mean VRP: ~3-4 percentage points
  • IV exceeded RV in ~85% of 30-day periods

    • This persistent positive VRP is the economic justification for premium selling strategies.

    What Different Gap Sizes Mean

    | IV vs RV | Interpretation | Trading Implication | IV > RV by 8+ pointsOptions are very expensiveStrong selling opportunity IV > RV by 3-7 pointsNormal premiumStandard selling conditions IV > RV by 0-2 pointsThin premiumSelective selling only IV ≈ RVFair valueNo clear edge either direction | IV < RV | Options are cheap | Consider buying strategies |

    Using the Comparison in Practice

    Before entering a premium sale: Check the current IV against recent realized volatility. If 30-day IV is 35% but 20-day realized vol is 30%, the premium covers a modest 5-point cushion. If IV is 35% and RV is 20%, you have a 15-point cushion — a much more attractive setup.

    For monitoring existing trades: If you sold options at 30% IV and realized volatility is running at 35%, the stock is moving more than expected. Tighten your management plan.

    For timing entries: When the IV-RV gap widens (IV rising while RV stays stable), the market is pricing in future turbulence that hasn't started yet. This can be a good time to sell, or a warning that a move is approaching.

    Lookback Period Matters

    Which RV timeframe you compare matters:

  • 10-day RV: Very recent activity. Good for short-dated options analysis.
  • 20-day RV: Standard comparison period. Matches roughly a monthly option.
  • 30-day RV: Slightly smoothed. Good for comparing against 30-DTE IV.
  • 60-day RV: Broader context. Useful for evaluating whether recent calm is temporary.

    • Compare IV against multiple RV timeframes. If IV is above all of them, options are genuinely expensive regardless of which period you reference.

    The RV Cone

    Advanced traders use a "volatility cone" — a chart showing the distribution of realized volatility across multiple timeframes (10, 20, 30, 60, 90 days) with percentile bands. Overlaying current IV on this cone instantly shows whether options are cheap or expensive relative to the full range of historical realized movement.

    Common Mistakes

    Comparing IV to the wrong RV period. If you're selling 45-DTE options, compare to 30-day RV, not 5-day RV. The timeframes should roughly match.

    Ignoring regime changes. If RV has been 15% for months but jumped to 25% this week, the low average RV is misleading. Recent RV matters more than distant RV.

    Treating the VRP as guaranteed. The 85% hit rate means 15% of the time, realized volatility exceeds implied. Those losses can be larger than typical gains. Position sizing and risk management remain essential.

    OptionsPilot provides real-time options pricing data, making it straightforward to evaluate whether current premiums offer an attractive spread over recent stock movement before you commit to a trade.