# Implied Volatility, Constant Maturity, At-The-Money ## Overview A continuous timeseries representing the annualized implied volatility of an option at constant maturity using at-the-money option contracts. The metrics are available for exchange-assets. Implied volatility ($$\sigma\_{imp}$$) is a metric derived from options contracts that quantifies the market’s expectation of future price fluctuations for an underlying asset. In standard option pricing models (such as Black-Scholes), $$\sigma\_{imp}$$ is the variable that equates the theoretical model price to the current market price of the option. Tracking $$\sigma\_{imp}$$ as a continuous timeseries presents two significant challenges regarding time decay and moneyness: 1. Time Decay ($$T$$): The time to expiration for any specific contract decreases linearly. If an option expires in $$30$$ days at time $$t$$, it will expire in $$29$$ days at time $$t+1$$. Comparing volatility day-over-day requires disentangling the effects of changing market conditions from the mechanical decay of time. 2. Moneyness ($$\frac{S}{K}$$): As the spot price of the underlying asset ($$S$$) fluctuates, the significance of a fixed strike price ($$K$$) changes. For example, a strike price of $$$60,000$$ represents a different risk profile when the underlying asset trades at $$$40,000$$ versus $$$59,000$$. To resolve these inconsistencies, we provide constant-maturity, at-the-money (ATM) implied volatility metrics. These synthetic metrics estimate the implied volatility for a hypothetical option that always has a fixed time horizon and a strike price equal to the current spot price. These implied volatility curves enable cross-sectional and timeseries comparison of volatility expectations across assets, independent of contract expiries or moneyness distortions. ## Metrics The implied volatility metrics across various combinations of tenor. The metrics follow the naming convention:\ \ `volatility_implied_atm_[tenor]_expiration` The tenor dimension and its values are: * `[tenor]`: `1d`, `2d`, `3d`, `7d`, `14d`, `21d`, `30d`, `60d`, `90d`, `120d`, `180d`, `270d`, `1y`
MetricDescriptionFrequencyCoverage
volatility_implied_atm_1d_expirationThe annualized estimated implied volatility of an option expiring 1 day in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_2d_expirationThe annualized estimated implied volatility of an option expiring 2 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_3d_expirationThe annualized estimated implied volatility of an option expiring 3 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_7d_expirationThe annualized estimated implied volatility of an option expiring 7 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_14d_expirationThe annualized estimated implied volatility of an option expiring 14 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_21d_expirationThe annualized estimated implied volatility of an option expiring 21 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_30d_expirationThe annualized estimated implied volatility of an option expiring 30 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_60d_expirationThe annualized estimated implied volatility of an option expiring 60 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_90d_expirationThe annualized estimated implied volatility of an option expiring 90 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_120d_expirationThe annualized estimated implied volatility of an option expiring 120 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_180d_expirationThe annualized estimated implied volatility of an option expiring 180 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_270d_expirationThe annualized estimated implied volatility of an option expiring 270 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
volatility_implied_atm_1y_expirationThe annualized estimated implied volatility of an option expiring 365 days in the future, using at the money option contracts with near-by expiration dates.1h, 1dπŸ”—
## Data Sources and Methodology The calculation creates a normalized value by interpolating between the implied volatility reported by exchanges for existing market contracts. The process is defined as follows: **1. Horizon Selection** \ \ For every observation, we define a target time horizon, $$T\_{target}$$ (e.g., 30 days, 90 days, or 365 days). **2. Contract Identification**\ \ We identify the market price of the underlying asset, $$S\_t$$, using the Coin Metrics Real-Time Reference Rate. We then select two sets of call options based on their expiration dates relative to the target:\ \ Near-Term Options: Expiration $$T\_{near} < T\_{target}$$\ \ Far-Term Options: Expiration $$T\_{far} > T\_{target}$$ **3. ATM Selection**\ \ From both the Near-Term and Far-Term sets, we select the specific contract where the strike price $$K$$ is closest to the spot price $$S\_t$$ (minimizing $$|S\_t - K|$$). This yields two reference implied volatilities:\ \ $$\sigma\_{near}$$: The implied volatility of the closest ATM option expiring before the target.\ \ $$\sigma\_{far}$$: The implied volatility of the closest ATM option expiring after the target. **4. Time-Weighted Interpolation**\ \ To determine the synthetic volatility at exactly $$T\_{target}$$, we calculate a weighted mean of $$\sigma\_{near}$$ and $$\sigma\_{far}$$. The weights are inversely proportional to the time difference between the option's expiration and the target date.\ \ Let $$\Delta t$$ represent the absolute time difference: $$ \Delta t\_{i} = | T\_{target} - T\_{expiration, i} | $$ The weight $$w\_i$$ for each option is calculated as: $$ w\_i = \frac{1}{\Delta t\_{i}} $$ **5. Final Calculation**\ \ The final implied volatility $$\sigma\_{target}$$ is the weighted average of the two selected options. This ensures that an option expiring closer to the target date exerts a stronger influence on the final metric than one further away: $$ \sigma\_{target} = \frac{w\_{near} \cdot \sigma\_{near} + w\_{far} \cdot \sigma\_{far}}{w\_{near} + w\_{far}} $$ ## Coverage {% embed url="" %} ## API Endpoints The metrics are served through the following endpoints: * [/timeseries/exchange-asset-metrics](https://docs.coinmetrics.io/api/v4/#tag/Timeseries/operation/getTimeseriesExchangeAssetMetrics) ## Examples #### Example for Exchange Asset Metrics A sample of the `volatility_implied_atm_30d_expiration` metric for the exchange\_asset `deribit-btc` from our `/timeseries/exchange-asset-metrics` API endpoint is provided below. You can view this example in your browser [here](https://api.coinmetrics.io/v4/timeseries/exchange-asset-metrics?exchange_assets=deribit-btc\&metrics=volatility_implied_atm_30d_expiration\&limit_per_exchange_asset=3\&frequency=1d\&api_key=YOUR_API_KEY). ```json [ { "exchange_asset": "deribit-btc", "time": "2025-12-09T00:00:00.000000000Z", "volatility_implied_atm_30d_expiration": "0.4708629" }, { "exchange_asset": "deribit-btc", "time": "2025-12-10T00:00:00.000000000Z", "volatility_implied_atm_30d_expiration": "0.4496676" }, { "exchange_asset": "deribit-btc", "time": "2025-12-11T00:00:00.000000000Z", "volatility_implied_atm_30d_expiration": "0.4313029" } ] ``` ## Frequently Asked Questions #### What units are the implied volatility metrics in? The metrics are presented in raw units. For instance, a value of `0.5223685` should be interpreted as `52.23685%`.