Implied vs Realised Volatility: What Options Are Actually Pricing

Implied vs Realised Volatility: What Options Are Actually Pricing

বাংলায় পড়ুন

Options traders often say volatility is “high” or “low”, but the statement is incomplete. High compared with what: the asset's own history, another expiry, a forthcoming event or the movement that eventually occurs?

The most useful comparison is between implied volatility (IV), which is backed out of current option prices, and realised volatility (RV), which measures how much the underlying asset has actually moved. They answer different questions and must be compared over matching horizons.

Learning objective

This tutorial explains how to:

1. Distinguish implied from realised volatility.
2. Convert annualised volatility into an approximate shorter-term move.
3. Compare the two measures without mistaking either for a directional forecast.
4. Build a risk checklist before using options around volatile events.

The calculations are educational approximations. They do not identify a guaranteed “cheap” or “expensive” option.

Implied volatility: the price input solved backwards

An option price reflects several inputs, including the underlying price, strike, time to expiry, interest rates, dividends and volatility. If the market price of the option is known, a pricing model can be run backwards to find the volatility level consistent with that price. That result is implied volatility.

IV is normally shown as an annualised percentage. A 30% IV does not mean the stock is forecast to rise 30%, fall 30% or remain inside a 30% band. It describes the scale of movement embedded in option prices under model assumptions. It contains no direction.

IV also varies across strikes and expiries. A one-month at-the-money option can have a different IV from a three-month option or a far out-of-the-money put. This creates a volatility term structure and skew. Referring to “the IV” without naming the expiry and strike can therefore hide important information.

Realised volatility: movement that already happened

Realised or historical volatility is calculated from actual price returns over a chosen period, commonly using the standard deviation of daily logarithmic returns and annualising it. It is backward-looking when calculated from past prices.

A 20-day RV describes the variability observed during those 20 sessions. It is not a forecast of the next 20 sessions. If the measurement window includes a crash or earnings gap, the number can remain elevated after the event even when current conditions have calmed.

For a fair ex-post comparison, traders compare the IV observed at the start of a period with the RV that occurs over the same future period. Comparing today's 30-day IV with the previous five days of RV may still provide context, but it is not a like-for-like forecast evaluation.

Step 1: Match the underlying, horizon and sampling method

Before comparing numbers, write down:

• The exact underlying asset.
• The option expiry and strike used for IV.
• Whether IV is at-the-money, a constant-maturity measure or a specific contract.
• The RV lookback or future evaluation window.
• Whether daily, intraday or close-to-close returns are used.
• Whether both figures are annualised using the same convention.

An index IV cannot be compared cleanly with a single-stock RV. A 30-day IV should not be judged against a one-year RV without recognising the horizon mismatch.

Step 2: Translate annualised volatility into a shorter horizon

For a rough trading-day estimate, scale annualised volatility by the square root of time:

Expected one-standard-deviation move ≈ annualised volatility × √(trading days ÷ 252)

For one trading day, √252 is close to 16. This produces the common “rule of 16”:

Approximate daily volatility ≈ annualised volatility ÷ 16

If IV is 32%, the implied average one-standard-deviation daily move is approximately 2%. This is not a daily limit and not a prediction that the next move will be exactly 2%. Actual returns can be much smaller or larger, and financial returns are not perfectly normally distributed.

For 21 trading days, the same 32% IV gives:

32% × √(21 ÷ 252) ≈ 9.24%

On a £100 share, that corresponds to an approximate one-standard-deviation scale of £9.24 over that horizon under simplified assumptions. It should not be presented as a guaranteed £90.76-to-£109.24 range.

Step 3: Compare IV with RV in context

Suppose 30-day at-the-money IV is 32% and the last 20 sessions' RV is 18%. The gap is 14 volatility points. It may be tempting to declare the options expensive, but the gap can have valid explanations:

• Earnings, a court decision or a regulatory announcement may fall inside the option's life.
• Recent calm trading may understate forward risk.
• Demand for downside protection may raise put IV.
• The two measures may use different horizons or calculation methods.
• Option sellers require compensation for gap and tail risk that cannot be continuously hedged.

IV above trailing RV is therefore a question to investigate, not an automatic signal to sell options. IV below trailing RV is not automatically a signal to buy them; the past high-volatility event may no longer be relevant.

Step 4: Separate direction, magnitude and path

An options view has at least three separate parts:

• Direction: whether the underlying rises or falls.
• Magnitude: how far it moves.
• Path and timing: when the move occurs and how price travels before expiry.

A trader can be right about direction and still lose on a long option if the move is too small, too late or offset by a fall in IV and time value. An option seller can be right that realised movement will be lower than implied and still suffer a large loss if the path includes a sharp gap or if risk is not limited.

Step 5: Define the volatility thesis and invalidation

A complete volatility thesis should say:

• Which IV measure appears high or low.
• What RV or event benchmark is being used.
• Why the gap exists.
• What would make the expected movement larger or smaller.
• How maximum loss is limited.
• When the thesis will be reviewed or closed.

For example: “One-month at-the-money IV is above its recent range because earnings occur before expiry. The thesis is that the post-event move will be smaller than the option market implies. The thesis is invalid if a new material catalyst appears or the planned maximum loss is reached.” This is a testable statement; “IV is high, so sell premium” is not.

Worked example

Consider a hypothetical £100 share with 21 trading days to the option's evaluation point:

• At-the-money IV: 32% annualised.
• Recent 21-day RV: 18% annualised.
• Approximate IV-scaled 21-day move: 32% × √(21/252) = 9.24%.
• Approximate RV-scaled 21-day movement: 18% × √(21/252) = 5.20%.

The option market is pricing a substantially larger movement scale than the recent realised history. The difference is 14 volatility points, but that does not reveal why.

Now assume an earnings announcement occurs in 10 days. The trader checks two additional observations: options expiring before earnings have 20% IV, while those expiring after earnings have 32% IV. The term structure suggests the event accounts for much of the premium.

A careful conclusion is: “The post-earnings expiry embeds more movement than both recent RV and the pre-event expiry.” An careless conclusion would be: “The option is overpriced and must fall.” The event could produce a larger-than-implied gap, and an uncovered short option could face losses far beyond the premium collected.

If the trader is evaluating a defined-risk structure costing £2.00 per share, the maximum premium at risk is £200 for one standard 100-share contract, before fees, provided the position is simply bought and not altered. That cash amount should still be assessed against the account's written risk budget. Complex spreads can carry assignment, liquidity and settlement risks that the simple maximum-loss figure may not fully describe in practice.

Common mistakes

Treating IV as a bullish or bearish signal

IV measures expected movement, not direction. Calls and puts can both become more expensive when uncertainty rises.

Comparing mismatched horizons

A one-week IV and one-year RV answer different questions. Match the window or state the mismatch explicitly.

Assuming high IV must revert immediately

IV can remain high or rise further when uncertainty increases. A percentile or rank describes history, not a ceiling.

Ignoring skew and term structure

At-the-money IV can look moderate while downside puts or a specific event expiry price much greater risk.

Selling undefined risk because premium looks rich

The premium received is limited; the loss on some short-option positions can be very large or theoretically unlimited.

Forgetting liquidity

Wide bid-ask spreads can make a modelled edge difficult to capture. Marking a position at the midpoint does not guarantee execution there.

Practical checklist

• Name the underlying, strike and expiry.
• Confirm whether IV is contract-specific or constant maturity.
• Match the IV and RV horizons as closely as possible.
• Convert annualised figures using a consistent time convention.
• Check earnings, economic releases and other events inside the expiry.
• Review volatility skew and term structure.
• Separate direction from expected magnitude.
• Include spread, fees and slippage.
• Calculate maximum loss and assignment exposure.
• Write the condition that invalidates the volatility thesis.

Sources and further reading

The Options Industry Council explains the distinction between historical and implied volatility and provides delayed comparison tools. Its guide to the rule of 16 describes the square-root-of-time shortcut and its limits. Cboe explains that the VIX measures 30-day expected S&P 500 volatility, while OCC publishes the formal Characteristics and Risks of Standardized Options.

For related concepts, read our guide to implied-volatility crush around events and options delta and gamma.

This tutorial was prepared with AI-assisted research and editorial review. It is educational information, not personalised investment advice. Options involve risk and are not suitable for every investor; no calculation or strategy guarantees a profit or prevents a loss.