IV Surface

What is this endpoint for?

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, MATIC, 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.

Endpoint

https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_surface

Parameters

• Short listed-maturities (e.g. 7 days time-to-maturity) are only available for individual exchange.

• 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).

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

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	The strike at which the IV has been computed. Not provided when the input is a delta list.	265.88827409960714
forward_log_moneyness	The associated forward log-moneyness. Not provided when the input is a delta list.	-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
interest_rate	The implied interest rate.	0.14954983972466698
current_spot	The underlying spot price at the value timestamp.	71717

Request examples

cURL

Use this example to calculate IV Surface using Deltas.

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

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

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

Use this example to calculate IV Surface using strikes.

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

Response examples

Deltas

{
    "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,
                "interest_rate":0.06444166091264596,
                "current_spot":58033.0026110549
             },
             {
                "implied_volatility":0.6010333506232379,
                "delta":0.8999999999999999,
                "interest_rate":0.06444166091264596,
                "current_spot":58033.0026110549
             }
          ]
       },
       {
          "value_time":"2024-09-12T10:00:00.000Z",
          "expiry":"2024-11-08T08:00:00.000Z",
          "time_to_expiry":0.15593607305936072,
          "implied_volatilities":[
             {
                "implied_volatility":0.6624300907047234,
                "delta":0.1,
                "interest_rate":0.06396819887540026,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.6181620638701805,
                "delta":0.2,
                "interest_rate":0.06396819887540026,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5977210831388879,
                "delta":0.30000000000000004,
                "interest_rate":0.06396819887540026,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5873014915704046,
                "delta":0.4,
                "interest_rate":0.06396819887540026,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5831399288267296,
                "delta":0.5,
                "interest_rate":0.06396819887540026,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5842407024308494,
                "delta":0.6,
                "interest_rate":0.06396819887540026,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.5912675169813805,
                "delta":0.7,
                "interest_rate":0.06396819887540026,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.6074281344387386,
                "delta":0.7999999999999999,
                "interest_rate":0.06396819887540026,
                "current_spot":58033.01112255454
             },
             {
                "implied_volatility":0.6449624313701908,
                "delta":0.8999999999999999,
                "interest_rate":0.06396819887540026,
                "current_spot":58033.01112255454
             }
          ]
       }
    ],
    "result":"success",
    "access":{
       "access_range":{
          "start_timestamp":1262304000000,
          "end_timestamp":1924991999000
       },
       "data_range":{
          "start_timestamp":1262304000000,
          "end_timestamp":1924991999000
       }
    }
 }

Forward log moneyness

{
   "query":{
      "base":"btc",
      "quote":"usd",
      "exchanges":[
         "drbt"
      ],
      "value_time":"2024-09-12T10:00:00.000Z",
      "data_version":"v2",
      "commodity":"analytics",
      "request_time":"2024-09-13T10:22:26.108Z"
   },
   "time":"2024-09-13T10:22:26.108Z",
   "timestamp":1726222946604,
   "complete_output":false,
   "data":[
      {
         "value_time":"2024-09-12T10:00:00.000Z",
         "expiry":"2024-09-16T01:36:00.000Z",
         "time_to_expiry":0.01,
         "implied_volatilities":[
            {
               "strike":35205.07731688165,
               "forward_log_moneyness":-0.5,
               "implied_volatility":1.219961822819801,
               "delta":0.9999840518413259,
               "gamma":9.862878922173833e-09,
               "interest_rate":0.029882129261974883,
               "current_spot":58026.01780838781
            },
            {
               "strike":58043.35980898536,
               "forward_log_moneyness":0,
               "implied_volatility":0.47173352808037106,
               "delta":0.5094088500573186,
               "gamma":0.00014570314379410554,
               "interest_rate":0.029882129261974883,
               "current_spot":58026.01780838781
            },
            {
               "strike":95697.3219399751,
               "forward_log_moneyness":0.5,
               "implied_volatility":0.9995009904225983,
               "delta":3.662902785528388e-07,
               "gamma":3.2466205143302194e-10,
               "interest_rate":0.029882129261974883,
               "current_spot":58026.01780838781
            }
         ]
      },
      {
         "value_time":"2024-09-12T10:00:00.000Z",
         "expiry":"2024-09-23T08:48:00.000Z",
         "time_to_expiry":0.03,
         "implied_volatilities":[
            {
               "strike":35258.65197953432,
               "forward_log_moneyness":-0.5,
               "implied_volatility":1.0227076131194504,
               "delta":0.998199924676951,
               "gamma":5.605337511004371e-07,
               "interest_rate":0.06064841675926235,
               "current_spot":58026.01780838785
            },
            {
               "strike":58131.68949487142,
               "forward_log_moneyness":0,
               "implied_volatility":0.5150355416768742,
               "delta":0.517788278262302,
               "gamma":7.69939568408782e-05,
               "interest_rate":0.06064841675926235,
               "current_spot":58026.01780838785
            },
            {
               "strike":95842.95297192968,
               "forward_log_moneyness":0.5,
               "implied_volatility":0.8521845389437603,
               "delta":0.00046039932852065535,
               "gamma":1.922319739897016e-07,
               "interest_rate":0.06064841675926235,
               "current_spot":58026.01780838785
            }
         ]
      },
      {
         "value_time":"2024-09-12T10:00:00.000Z",
         "expiry":"2024-09-30T16:00:00.000Z",
         "time_to_expiry":0.05,
         "implied_volatilities":[
            {
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         "value_time":"2024-09-12T10:00:00.000Z",
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   ],
   "result":"success",
   "access":{
      "access_range":{
         "start_timestamp":1262304000000,
         "end_timestamp":1924991999000
      },
      "data_range":{
         "start_timestamp":1262304000000,
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   }
}

Strikes

{
   "query":{
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      "quote":"usd",
      "exchanges":[
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      ],
      "value_time":"2024-09-12T10:00:00.000Z",
      "data_version":"v2",
      "commodity":"analytics",
      "request_time":"2024-09-13T10:31:21.687Z"
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   "time":"2024-09-13T10:31:21.687Z",
   "timestamp":1726223482124,
   "complete_output":false,
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