# 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`

Metric	Description	Frequency	Coverage
`volatility_implied_atm_1d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_2d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_3d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_7d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_14d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_21d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_30d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_60d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_90d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_120d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_180d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_270d_expiration`	The 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, 1d	🔗
`volatility_implied_atm_1y_expiration`	The 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, 1d	🔗

## 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%`. --- # Agent Instructions: Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter: ``` GET https://gitbook-docs.coinmetrics.io/market-data/market-data-overview/volatility/implied-volatility.md?ask= ``` The question should be specific, self-contained, and written in natural language. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.