> For the complete documentation index, see [llms.txt](https://docs.kaiko.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.kaiko.com/rest-api/analytics/derivatives-risk-indicators/implied-volatility-calculation-surface.md).

# Implied volatility calculation - surface

{% hint style="info" %}

### This data is included in the following Kaiko packages:

* Kaiko Derivatives Risk Indicators \[Advanced Tier]
  {% endhint %}

### What is this endpoint for? <a href="#what-is-this-endpoint-for" id="what-is-this-endpoint-for"></a>

The IV surface endpoint lets you calculate volatility from options market prices. Feed the endpoint a set of maturity dates or timeframes for when options can be exercised, and you'll receive a volatility surface, which shows how volatility changes over different dates and prices.

You can get volatility estimates based on:

* A specific set of strike prices
* A forward-log-moneyness grid
* A specific set of delta values
* A delta grid

The calculation methodology leverages space and time interpolation.

**Currently supported assets and exchanges:**

* BTC, ETH, SOL, and XRP on Deribit.
* BTC, ETH on OKX.
* BTC, ETH on Deribit & OKX (aggregated).

If you need data from other exchanges, we can add them on request.

Read our Implied Volatility Methodology [here](https://25446524.fs1.hubspotusercontent-eu1.net/hubfs/25446524/Factsheets/Kaiko%20Implied%20Volatility%20Methodology.pdf).

### Endpoint

{% code overflow="wrap" %}

```http
https://{eu/us}.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_surface
```

{% endcode %}

### Path Parameters

| Parameter | Required? | Example                       |
| --------- | --------- | ----------------------------- |
| `region`  | Yes       | Choose between `eu` and `us`. |

### Query Parameters

{% hint style="warning" %}

* Short listed-maturities (e.g. 7 days time-to-maturity) are only available for individual exchanges.
* Time extrapolation is not permitted. I.e. the shortest requested expiry should be after the exchange's shortest expiry, and the furthest requested expiry must be before the exchange's latest expiry. If these conditions are not met, only a partial surface will be returned within the available expiry range. The completeness of the output is indicated in the `complete_output` field.
* Strikes and forward-log-moneynesses are only available when retrieving implied volatilities by strikes or forward-log-moneynesses (not by delta).
  {% endhint %}

<table><thead><tr><th width="136">Parameter</th><th width="154">Required</th><th width="300">Description</th><th>Example</th></tr></thead><tbody><tr><td><code>base</code></td><td>Yes</td><td>The desired base as the underlying of the options.<br><br>See asset support above.</td><td><code>btc</code>, <code>eth</code></td></tr><tr><td><code>quote</code></td><td>Yes</td><td>The desired quote as the underlying of the options.<br><br>See asset support above.</td><td><code>usd</code></td></tr><tr><td><code>exchanges</code></td><td>Yes</td><td>The desired exchange as source of options data.<br><br>See exchange support above.</td><td><code>drbt</code></td></tr><tr><td><code>value_time</code></td><td>Yes</td><td>The time at which to compute implied volatilities<br><br>The time <em>t</em> should be smaller than the lowest requested expiry.</td><td><code>2022-06-25T16:00:00.000Z</code></td></tr><tr><td><code>expiry_list</code></td><td>Yes, if the set of parameters (<code>tte_min</code>, <code>tte_max</code>, <code>tte_step</code>) is not used.</td><td><p>The expiries for which the implied volatilities are to be computed. Expiries can be listed or non-listed ones.</p><ul><li>Expiries should be between minimum and maximum listed maturities on exchange. If not, a partial output will be returned.</li><li>Either <code>expiry_list</code> or (<code>tte_min</code>, <code>tte_max</code>, <code>tte_step</code>) should be filled.</li></ul></td><td><code>expiry_list=2022-08-28T08:00:00.000Z, 2022-08-30T08:00:00.000Z</code><br>or <code>tte_min=0.034288&#x26;tte_max=1&#x26;tte_step=0.02</code></td></tr><tr><td><code>tte_min</code></td><td>Yes, if <code>expiry_list</code> is not used. To be used along with <code>tte_max</code>, <code>tte_step</code>.</td><td><p>Minimum time-to-expiry on the time grid.</p><ul><li>Strictly positive value allowed.</li><li>If the `tte_min` is below the time to expiry associated with the minimum listed maturity, partial output will be returned.</li><li>Either <code>expiry_list</code> or (<code>tte_min</code>, <code>tte_max</code>, <code>tte_step</code>) should be filled.</li></ul></td><td><code>0.034288</code></td></tr><tr><td><code>tte_max</code></td><td>Yes, if <code>expiry_list</code> is not used. To be used along with <code>tte_min</code>, <code>tte_step</code>.</td><td><p>Maximum time-to-expiry on the time grid.</p><ul><li>Strictly positive value above the `tte_min`.</li><li>If the `tte_max` is above the time to expiry associated with the maximum listed maturity, partial output will be returned.</li><li>Either <code>expiry_list</code> or <code>(tte_min, tte_max,tte_step)</code> should be filled.</li></ul></td><td><code>1</code></td></tr><tr><td><code>tte_step</code></td><td>Yes, if <code>expiry_list</code> is not used. To be used along with <code>tte_min</code>, <code>tte_max</code>.</td><td><p>Step between two time-to-expiries in time grid.</p><ul><li>Strictly positive value allowed.</li><li>Either <code>expiry_list</code> or <code>(tte_min, tte_max, tte_step)</code> should be filled.</li></ul></td><td><code>0.02</code></td></tr><tr><td><code>strike_list</code></td><td>Yes, if the set of parameters (<code>f_log_min</code>, <code>f_log_max</code>, <code>f_log_step</code>) or <code>deltas</code> or the set of parameters (<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) are not used.</td><td><p>The strike prices for which the implied volatilities are to be computed. Strike prices can be listed or non-listed ones.</p><ul><li>Strictly positives values allowed.</li><li>Either <code>strike_list</code> , (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>), <code>deltas</code> or<br>(<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) should be filled.</li></ul></td><td><code>strike_list=25000, 29150, 29155, 29160</code><br>or <code>f_log_m_min=-1.5&#x26;f_log_m_max=1.5&#x26;f_log_m_step=0.05</code></td></tr><tr><td><code>f_log_m_min</code></td><td>Yes, if <code>strike_list</code> or <code>deltas</code> or the set of parameters (<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) are not used.<br>To be used along with <code>f_log_m_max</code>, <code>f_log_m_step</code>.</td><td><p>Minimum forward log-moneyness on the space grid.<br></p><ul><li>Either <code>strike_list</code> , (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>), <code>deltas</code> or<br>(<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) should be filled.</li></ul></td><td><code>-1.5</code></td></tr><tr><td><code>f_log_m_max</code></td><td>Yes, if <code>strike_list</code> or <code>deltas</code> or the set of parameters (<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) are not used.<br>To be used along with <code>f_log_m_min</code>, <code>f_log_m_step</code>.</td><td><p>Maximum forward log-moneyness on the space grid.<br></p><ul><li>Either <code>strike_list</code> , (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>), <code>deltas</code> or<br>(<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) should be filled.</li></ul></td><td><code>1</code></td></tr><tr><td><code>f_log_m_step</code></td><td>Yes, if <code>strike_list</code> or <code>deltas</code> or the set of parameters (<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) are not used.<br>To be used along with <code>f_log_m_min</code>, <code>f_log_m_max</code>.</td><td><p>Step between two forward log moneyness in space grid.</p><ul><li>Either <code>strike_list</code> , (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>), <code>deltas</code> or<br>(<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) should be filled.</li></ul></td><td><code>0.02</code></td></tr><tr><td><code>deltas</code></td><td>Yes, if <code>strike_list</code> or the sets of parameters <code>(delta_min, delta_max, delta_step)</code> or (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>) are not used.</td><td><p>The delta levels (of a Call option) for which the implied volatilities are to be computed.</p><ul><li>Only delta values between <code>0.01</code> and <code>0.99</code> are allowed.</li><li>Either <code>strike_list</code> , (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>), <code>deltas</code> or<br>(<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) should be filled.</li></ul></td><td><code>deltas=0.25,0.5,0.75</code></td></tr><tr><td><code>delta_min</code></td><td>Yes, if <code>strike_list</code> or <code>deltas</code> or the set of parameters (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>) are not used. To be used along with <code>delta_max</code>, <code>delta_step</code>.</td><td><p>Minimum delta (of a Call option) on the space grid.</p><ul><li>Only delta values between <code>0.01</code> and <code>0.99</code> are allowed.</li><li>Either <code>strike_list</code> , (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>), <code>deltas</code> or<br>(<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) should be filled.</li></ul></td><td><code>0.01</code></td></tr><tr><td><code>delta_max</code></td><td>Yes, if <code>strike_list</code> or <code>deltas</code> or the set of parameters (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>) are not used. To be used along with <code>delta_min</code>, <code>delta_step</code>.</td><td><p>Maximum delta (of a Call option) on the space grid.</p><ul><li>Only delta values between <code>0.01</code> and <code>0.99</code> are allowed.</li><li>Either <code>strike_list</code> , (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>), <code>deltas</code> or<br>(<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) should be filled.</li></ul></td><td><code>0.99</code></td></tr><tr><td><code>delta_step</code></td><td>Yes, if <code>strike_list</code> or <code>deltas</code> or the set of parameters (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>) are not used. To be used along with <code>delta_min</code>, <code>delta_max</code>.</td><td><p>Step between two deltas (of a Call option) on the space grid.</p><ul><li>Either <code>strike_list</code> , (<code>f_log_m_min</code>, <code>f_log_m_max</code>, <code>f_log_m_step</code>), <code>deltas</code> or<br>(<code>delta_min</code>, <code>delta_max</code>, <code>delta_step</code>) should be filled.</li></ul></td><td></td></tr></tbody></table>

### Fields

| Field                   | Description                                                                                                               | Example                   |
| ----------------------- | ------------------------------------------------------------------------------------------------------------------------- | ------------------------- |
| complete\_output        | This indicates whether the output covers the entire requested range within the listed expiries, or only the valid subset. | True                      |
| `value_time`            | The time in parameter                                                                                                     | `2022-06-25T16:00:00Z`    |
| `expiry`                | The expiry at which the IV has been interpolated.                                                                         | `2022-08-28T08:00:00Z`    |
| `time_to_expiry`        | The associated time-to-expiry (in year).                                                                                  | `0.17442922374429223`     |
| `strike`                | <p>The strike at which the IV has been computed.<br>Not provided when the input is a delta list.</p>                      | `265.88827409960714`      |
| `forward_log_moneyness` | <p>The associated forward log-moneyness.<br>Not provided when the input is a delta list.</p>                              | `-1.5`                    |
| `implied_volatility`    | The calibrated and interpolated implied volatilities.                                                                     | `1.8088997727784055`      |
| `delta`                 | The first derivative of the price (of a Call option) with regards to the underlying price                                 | `-0.009058250602524742`   |
| `gamma`                 | The second derivative of the price with regards to the underlying price                                                   | `0.000027152549142705487` |
| `vega`                  | The first derivative of the price with regards to implied volatility.                                                     | `18.73162001892539`       |
| `theta`                 | The first derivative of the price with regards to the passage of time (or time to expiration).                            | `-194.40147413397432`     |
| `interest_rate`         | The implied interest rate.                                                                                                | `0.14954983972466698`     |
| `current_spot`          | The underlying spot price at the value timestamp.                                                                         | `71717`                   |

### Request examples

{% tabs %}
{% tab title="cURL" %}
**Use this example to calculate IV Surface using Deltas.**

{% code overflow="wrap" %}

```url
https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_surface?base=btc&quote=usd&exchanges=drbt%2Cokex&value_time=2024-09-12T10%3A00%3A00.000Z&expiry_list=2024-09-20T08%3A00%3A00.000Z%2C2024-09-27T08%3A00%3A00.000Z%2C2024-10-04T08%3A00%3A00.000Z%2C2024-10-25T08%3A00%3A00.000Z%2C2024-11-08T08%3A00%3A00.000Z&delta_min=0.1&delta_max=0.9&delta_step=0.1
```

{% endcode %}

**Use this example to calculate IV Surface using forward log moneyness.**

{% code overflow="wrap" %}

```
https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_surface?base=btc&quote=usd&exchanges=drbt&value_time=2024-09-12T10%3A00%3A00.000Z&tte_min=0.01&tte_max=1.&tte_step=0.02&f_log_m_min=-0.5&f_log_m_max=0.5&f_log_m_step=0.5
```

{% endcode %}

**Use this example to calculate IV Surface using strikes.**

{% code overflow="wrap" %}

```url
https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_surface?base=btc&quote=usd&exchanges=drbt&value_time=2024-09-12T10%3A00%3A00.000Z&tte_min=0.01&tte_max=1.&tte_step=0.02&strike_list=55000%2C56000%2C57000%2C58000%2C59000%2C60000
```

{% endcode %}
{% endtab %}
{% endtabs %}

### Response examples

{% code overflow="wrap" %}

```json
{
    "query":{
       "base":"btc",
       "quote":"usd",
       "exchanges":[
          "drbt",
          "okex"
       ],
       "value_time":"2024-09-12T10:00:00.000Z",
       "data_version":"v2",
       "commodity":"analytics",
       "request_time":"2024-09-12T17:12:07.699Z"
    },
    "time":"2024-09-12T17:12:07.699Z",
    "timestamp":1726161128874,
    "complete_output":true,
    "data":[
       {
          "value_time":"2024-09-12T10:00:00.000Z",
          "expiry":"2024-09-20T08:00:00.000Z",
          "time_to_expiry":0.021689497716894976,
          "implied_volatilities":[
             {
                "implied_volatility":0.55567045411767,
                "delta":0.1,
                "interest_rate":0.05222290146213202,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5304086533216835,
                "delta":0.2,
                "interest_rate":0.05222290146213202,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5204807466788227,
                "delta":0.30000000000000004,
                "interest_rate":0.05222290146213202,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5176080670107802,
                "delta":0.4,
                "interest_rate":0.05222290146213202,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5198235126846833,
                "delta":0.5,
                "interest_rate":0.05222290146213202,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5271474253673343,
                "delta":0.6,
                "interest_rate":0.05222290146213202,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5412722397557681,
                "delta":0.7,
                "interest_rate":0.05222290146213202,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5672860200574902,
                "delta":0.7999999999999999,
                "interest_rate":0.05222290146213202,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.6234279466167519,
                "delta":0.8999999999999999,
                "interest_rate":0.05222290146213202,
                "current_spot":58033.01112255454
             }
          ]
       },
       {
          "value_time":"2024-09-12T10:00:00.000Z",
          "expiry":"2024-09-27T08:00:00.000Z",
          "time_to_expiry":0.0408675799086758,
          "implied_volatilities":[
             {
                "implied_volatility":0.5621097108504748,
                "delta":0.1,
                "interest_rate":0.052497499225334636,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5272061410113572,
                "delta":0.2,
                "interest_rate":0.052497499225334636,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5131506051610666,
                "delta":0.30000000000000004,
                "interest_rate":0.052497499225334636,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5082456534252546,
                "delta":0.4,
                "interest_rate":0.052497499225334636,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5095651826004636,
                "delta":0.5,
                "interest_rate":0.052497499225334636,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.51677777797711,
                "delta":0.6,
                "interest_rate":0.052497499225334636,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5314642342464321,
                "delta":0.7,
                "interest_rate":0.052497499225334636,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5587288797341338,
                "delta":0.7999999999999999,
                "interest_rate":0.052497499225334636,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.6167183766301421,
                "delta":0.8999999999999999,
                "interest_rate":0.052497499225334636,
                "current_spot":58033.01112255454
             }
          ]
       },
       {
          "value_time":"2024-09-12T10:00:00.000Z",
          "expiry":"2024-10-04T08:00:00.000Z",
          "time_to_expiry":0.06004566210045662,
          "implied_volatilities":[
             {
                "implied_volatility":0.5666208561497174,
                "delta":0.1,
                "interest_rate":0.06524195117082478,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5323692982650756,
                "delta":0.2,
                "interest_rate":0.06524195117082478,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5186955773995799,
                "delta":0.30000000000000004,
                "interest_rate":0.06524195117082478,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5138985541028067,
                "delta":0.4,
                "interest_rate":0.06524195117082478,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5150201900956664,
                "delta":0.5,
                "interest_rate":0.06524195117082478,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5216164561118771,
                "delta":0.6,
                "interest_rate":0.06524195117082478,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5349940736116142,
                "delta":0.7,
                "interest_rate":0.06524195117082478,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5595467577751186,
                "delta":0.7999999999999999,
                "interest_rate":0.06524195117082478,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.6109550611499716,
                "delta":0.8999999999999999,
                "interest_rate":0.06524195117082478,
                "current_spot":58033.01112255454
             }
          ]
       },
       {
          "value_time":"2024-09-12T10:00:00.000Z",
          "expiry":"2024-10-25T08:00:00.000Z",
          "time_to_expiry":0.11757990867579908,
          "implied_volatilities":[
             {
                "implied_volatility":0.5922138420961504,
                "delta":0.1,
                "interest_rate":0.06444166091264596,
                "current_spot":58033.0026110549
             },
             {
                "implied_volatility":0.5520922097809197,
                "delta":0.2,
                "interest_rate":0.06444166091264596,
                "current_spot":58033.0026110549
             },
             {
                "implied_volatility":0.5329630080551225,
                "delta":0.30000000000000004,
                "interest_rate":0.06444166091264596,
                "current_spot":58033.0026110549
             },
             {
                "implied_volatility":0.5231218680220053,
                "delta":0.4,
                "interest_rate":0.06444166091264596,
                "current_spot":58033.0026110549
             },
             {
                "implied_volatility":0.5194493140150083,
                "delta":0.5,
                "interest_rate":0.06444166091264596,
                "current_spot":58033.0026110549
             },
             {
                "implied_volatility":0.5213876755567547,
                "delta":0.6,
                "interest_rate":0.06444166091264596,
                "current_spot":58033.0026110549
             },
             {
                "implied_volatility":0.5302377211015243,
                "delta":0.7,
                "interest_rate":0.06444166091264596,
                "current_spot":58033.0026110549
             },
             {
                "implied_volatility":0.550749699660159,
                "delta":0.7999999999999999,
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    "result":"success",
    "access":{
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       "data_range":{
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       }
    }
 }
```

{% endcode %}

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   "result":"success",
   "access":{
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}
```


---

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