Implied vs. Realized Volatility: A Reproducible Comparison

For educational purposes only; not investment advice.

Direct answer

Implied volatility (IV) is an annualized model input inferred from an option quote at a particular time, strike, and expiry. Realized volatility (RV) is an annualized statistic calculated from returns observed over a specified interval. Entry IV is observable now; the matching future RV is known only after that interval ends.

A useful comparison must freeze the underlying, observation time, horizon, return sampling, price adjustment, and annualization convention. Comparing 30-day IV with an arbitrary one-year historical volatility number does not test the same period. Even a correctly measured IV - RV difference is a pricing diagnostic, not a formula for option profit.

IV is inferred from option prices under a model; RV is calculated from an observed return series. Neither is a guaranteed forecast.

Build a comparison that can be reproduced

Before observing the outcome, record:

1. the underlying, quote timestamp, bid/mid/ask convention, strike, and expiry;
2. whether IV is one contract’s value, an ATM interpolation, or a broader variance measure;
3. the exact future dates and the price series to be sampled;
4. whether returns are close-to-close, intraday, or another estimator;
5. the trading-day count and treatment of dividends, splits, missing prices, and the sample mean.

For adjusted closing prices, daily log return is:

r_t = ln(S_t / S_(t-1))

One common sample estimator using n returns is:

RV = √[252 / (n - 1) × Σ(r_i - r̄)²]

Some systems use simple returns, omit the mean, use 250 rather than 252, or estimate variation from intraday observations. None is universally correct for every purpose. The important rule is to state the estimator and apply it consistently.

Volatility points are intuitive, but option valuation is nonlinear. Analysts therefore also compare annualized variance:

volatility spread = IV_entry - RV_future

variance spread = IV_entry² - RV_future²

Past RV can provide context for today’s quote, but it is not the ex-post outcome for the option’s future horizon. IV can also embed compensation for jump and volatility risk, supply and demand, skew, liquidity, rates, dividends, and model assumptions. It need not equal a pure statistical forecast.

Measurement and trade-attribution example

Suppose a 30-calendar-day ATM option measure has entry IV of 32%. The protocol fixes the next 20 adjusted close-to-close log returns. After the interval, their daily sample standard deviation is 1.40%:

RV = 1.40% × √252 ≈ 22.23%

The volatility spread is approximately:

32.00% - 22.23% = 9.77 percentage points

The annualized variance comparison is:

0.32² - 0.2223² ≈ 0.1024 - 0.0494 = 0.0530

This result says the selected implied input exceeded the subsequently measured close-to-close variation. It does not establish what any option position earned.

For example, assume an unhedged strike-$100 straddle was sold for $7.50 with a 100-share multiplier. If the stock expires at $105, its intrinsic payoff is $5.00, so gross expiration result is ($7.50 - $5.00) × 100 = $250. If it expires at $112, payoff is $12.00, so gross result is ($7.50 - $12.00) × 100 = -$450. Fees, early exits, exercise, and assignment are excluded.

A Delta-hedged position requires a different attribution. Its result depends on when hedges occur, which price is used, Gamma weighting along the path, gaps, changing Greeks, financing, and transaction costs. Daily close-to-close RV cannot reconstruct those cash flows by itself.

Practical review table

Item	Entry record	Outcome record
Horizon	Quote time through fixed end time	Same dates only
Volatility	IV method, strike, expiry, quote side	RV estimator and observations
Market structure	Skew, event calendar, spread	Jumps, closures, corporate actions
Position	Contracts, Greeks, hedge rule	Payoff, hedge cash flows, costs

Risks and limitations

• Look-ahead bias: selecting the estimator or window after seeing the outcome invalidates the comparison.
• Horizon mismatch: calendar days, trading days, and time to expiry must describe the same interval.
• Sampling mismatch: close-to-close returns omit intraday paths; high-frequency estimates introduce their own noise.
• Surface mismatch: one strike’s IV, ATM IV, a volatility index, and a variance-swap rate are not interchangeable.
• Annualization mismatch: mixing 252-day, 365-day, or product-specific conventions distorts the result.
• Jump and event risk: a small number of gaps can dominate option losses and hedging results.
• Execution risk: bid-ask spreads, hedge slippage, commissions, borrow, and financing can consume an apparent edge.
• Model risk: inferred IV changes with pricing inputs and assumptions; it is not directly observed volatility.
• Short-option risk: losses, margin requirements, exercise, and assignment can exceed premium received.

Common misconceptions

• “IV is the market’s exact forecast.” It is an option-price-implied input and may include risk premiums and market frictions.
• “Future RV is known at entry.” Only historical estimates are known; matched future RV is ex-post.
• “IV above RV proves every option was expensive.” Strike, skew, payoff, path, and execution still matter.
• “Selling volatility wins whenever IV exceeds RV.” An unhedged contract can lose despite that statistical comparison.
• “Volatility spread and variance spread are the same.” 32% - 22.23% differs from 0.32² - 0.2223².
• “One RV number describes the whole path.” Equal summary RV can arise from economically different sequences and jumps.
• “ATM IV represents the entire surface.” Calls and puts across strikes and expiries can imply different values.
• “Delta hedging removes all other risks.” Discrete rebalancing, Gamma, costs, gaps, and changing inputs remain.

Related topics

• IV and RV overview
• Implied volatility
• Historical volatility
• Delta hedging

Authoritative sources

• Characteristics and Risks of Standardized Options — OCC
• Options Basics — Cboe Options Institute
• Expected Stock Returns and Variance Risk Premia — Bollerslev, Tauchen, and Zhou, The Review of Financial Studies
• The Pricing of Options and Corporate Liabilities — Black and Scholes, Journal of Political Economy