Implied versus Realized Volatility

Implied volatility is the volatility input that makes a chosen pricing model reproduce an observed option price. Realized volatility measures variation in observed returns over a specified interval. IV is inferred from a current price; realized volatility is calculated from a price path.

Two measurement processes

To estimate IV, specify the option’s price, strike, time, underlying, rates, distributions and exercise treatment. Wide quotes can imply a range of IV values. A model’s IV is not a direct measurement of traders’ beliefs: it also reflects risk compensation, market conditions and model assumptions.

For one common historical estimator, calculate daily log returns ln(Pt/Pt−1), take their sample standard deviation and multiply by √252. That convention uses 252 trading observations per year. Other methods use intraday returns, different annualization or no demeaning; report the convention rather than treating all realized-volatility numbers as interchangeable.

A numerical measurement example

If daily log-return sample standard deviation is 1.2%, annualized historical volatility under this convention is 0.012 × √252 = 19.05%. That describes the chosen sample. It does not assert that the next month will realize 19.05%.

Suppose a 30-day option is quoted at 25% IV today. Comparing it with the last month’s 19.05% volatility is a backward-looking benchmark. Comparing it with volatility realized over the next 30 days is a forward outcome study that cannot be completed today. A backtest that chooses trades using that future result has look-ahead bias.

Align horizon, timestamps and returns

Check whether overnight gaps are included, whether closing prices are adjusted consistently for splits and dividends, and whether nontrading days enter the annualization. Compare matching horizons where possible. An earnings jump inside one sample but outside another can dominate the difference.

Do not compare a deep-out-of-the-money put’s skewed IV with a broad at-the-money IV index without explaining the difference. Likewise, annualized volatility is a standard-deviation rate, not the probability of a particular maximum loss.

Trading the difference is not automatic

Even if future realized volatility is below today’s IV, an unhedged short option can lose from a directional move. A delta-hedged option has its own gamma weighting, hedge schedule, jumps, financing and costs. The realized-volatility statistic alone does not reconstruct those cash flows.

Use the IV-versus-realized comparison as one part of a clearly specified strategy. Record the entry price and hedge rule, then evaluate net P/L from the actual sequence of option and underlying transactions. That keeps a descriptive volatility comparison separate from a claim of an achievable return.