Implied volatility calculation - smile

If you need implied volatilities for expiry dates that are not listed, you can use the "implied volatility surface" endpoint to calculate this.

What is this endpoint for?

The IV Smile endpoint lets you calculate volatility on a minute-by-minute basis from options market prices. The endpoint returns a volatility curve for a specific expiry date.

You can get volatility estimates by providing the following information:

Strikes
Forward-log-moneyness
Deltas

The calculation methodology leverages space 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.

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

Endpoint

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

Parameters

Parameter

Required

Description

Example

base

Yes

The desired base as the underlying of the options. See supported assets above.

btc, eth

quote

Yes

The desired quote as the underlying of the options. usd or usdc

usd

value_time

Yes

The time at which to compute implied volatilities The time t should be smaller than the expiry T

2022-09-20T16:15:00.000Z

expiry

Yes

The expiry for which the implied volatilities are to be computed Must be an existing expiry on the selected exchange and tradable at the time of the computation.

2022-12-30T08:00:00.000Z

strikes

Yes, if neither forward_log_moneynesses nor deltas parameters are used.

The strike prices for which the implied volatilities are to be computed. Strike prices can be existing or non-existing ones (space interpolation included) Either strikes or forward_log_moneynesses or deltas should be filled.

singular: 10000 plural: 10000,15000,20000

forward_log_moneynesses

Yes, if neither strikes nor deltas parameters are used.

The forward log moneyness for which the implied volatilities are to be computed. Either strikes, forward_log_moneynesses or deltas should be filled.

singular: 1 plural: -1,-0.5,0,0.5,1

deltas

Yes, if neither forward_log_moneynesses nor strikes parameters are used.

The delta levels (of a Call option) for which the implied volatilities are to be computed. Either strikes, forward_log_moneynesses or deltas should be filled.

exchanges

The desired exchange as source of options data. See supported exchanges above.

drbt

Fields

Field

Description

Example

value_time

The time in parameter

2022-09-20T16:15:00.000Z

expiry

The expiry in parameter

2022-12-30T00:00:00.000Z

time_to_expiry

The associated time to expiry in year

0.27580868156450355

implied_volatilities

The list of requested implied volatilities

[{"strike": 40000, "forward_log_moneyness": 0.7348555803648208, "implied_volatility": 0.7341747093260883, "delta": 0.04334612697660922, "gamma": 0.000012437991693543254}, {"strike": 20000, "forward_log_moneyness": 0.041708399804875465, "implied_volatility": 0.6670092468551713, "delta": 0.5223606946028295, "gamma": 0.00005929353471794603}, ... ]

delta

The first derivative of the price with regards to the underlying price.

2.8863019124747424e-7

gamma

The second derivative of the price with regards to the underlying price.

2.416523346501216e-10

current_spot

The underlying spot price at the value timestamp.

71717

interest_rate

The implied interest rate.

0.14954983972466698

Request examples

Use this example to calculate IV using deltas.

curl --compressed -H 'Accept: application/json' -H 'X-Api-Key: <client-api-key>' \
'https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_smile?base=btc&quote=usd&value_time=2024-06-07T12:00:00.000Z&expiry=2024-06-28T00:00:00.000Z&exchanges=drbt&deltas=0.25,0.5,0.75'

Use this example to calculate IV using forward log moneyness.

https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_smile?base=btc&quote=usd&exchanges=drbt,okex&value_time=2024-09-12T10:00:00.000Z&expiry=2024-09-27T08:00:00.000Z&forward_log_moneynesses=-1,-0.5,0,0.5,1

Use this example to calculate IV using strikes.

https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_smile?base=btc&quote=usd&exchanges=drbt&value_time=2024-09-12T10:00:00.000Z&expiry=2024-09-27T08:00:00.000Z&strikes=30000,50000,60000,70000,90000

Use this example to calculate IV using deltas

import http.client
import json

# Enter your Kaiko API Key
api_key = "KAIKO_API_KEY"
api_host = "us.market-api.kaiko.io"
api_base_endpoint = "/v2/data/analytics.v2/implied_volatility_smile"
# Start of mandatory parameter configuration
mandatory_params = {
    "base": "btc",
    "quote": "usd",
    "value_time": "2024-06-07T12:00:00.000Z",
    "expiry": "2024-06-28T00:00:00.000Z",
    "deltas": "0.25,0.5,0.75",
}
# End of mandatory parameter configuration
# Start of optional parameter configuration
optional_params = {
    "exchanges": "drbt"
}
# End of optional parameter configuration
conn = http.client.HTTPSConnection(api_host)
headers = {
    "X-Api-Key": api_key,
    "Accept": "application/json"
}

all_params = {**mandatory_params, **optional_params}

url_params = []
for param, value in all_params.items():
    url_params.append(f"{param}={value}")
url_params = '&'.join(url_params)

endpoint_with_params = f"{api_base_endpoint}?{url_params}"
# Pagination for next pages
all_data = []
next_url = endpoint_with_params
while next_url:
    conn.request("GET", next_url, headers=headers)
    response = conn.getresponse()
    data = json.loads(response.read().decode("utf-8"))
    all_data.extend(data.get("data", []))
    print(f"Fetched {len(data.get('data', []))} datapoints. Total: {len(all_data)}")
    next_url = data.get("next_url", "").replace("https://us.market-api.kaiko.io", "")
    if not next_url:
        break
conn.close()
print(f" datapoints fetched: {(all_data)}")

Use this example to calculate IV using forward log moneyness

import http.client
import json

# Enter your Kaiko API Key
api_key = "KAIKO_API_KEY"
api_host = "us.market-api.kaiko.io"
api_base_endpoint = "/v2/data/analytics.v2/implied_volatility_smile"
# Start of mandatory parameter configuration
mandatory_params = {
    "base": "btc",
    "quote": "usd",
    "value_time": "2024-06-07T12:00:00.000Z",
    "expiry": "2024-06-28T00:00:00.000Z",
    "forward_log_moneynesses": "1,-0.5,0,0.5,1",
}
# End of mandatory parameter configuration
# Start of optional parameter configuration
optional_params = {
    "exchanges": "drbt"
}
# End of optional parameter configuration
conn = http.client.HTTPSConnection(api_host)
headers = {
    "X-Api-Key": api_key,
    "Accept": "application/json"
}

all_params = {**mandatory_params, **optional_params}

url_params = []
for param, value in all_params.items():
    url_params.append(f"{param}={value}")
url_params = '&'.join(url_params)

endpoint_with_params = f"{api_base_endpoint}?{url_params}"
# Pagination for next pages
all_data = []
next_url = endpoint_with_params
while next_url:
    conn.request("GET", next_url, headers=headers)
    response = conn.getresponse()
    data = json.loads(response.read().decode("utf-8"))
    all_data.extend(data.get("data", []))
    print(f"Fetched {len(data.get('data', []))} datapoints. Total: {len(all_data)}")
    next_url = data.get("next_url", "").replace("https://us.market-api.kaiko.io", "")
    if not next_url:
        break
conn.close()
print(f" datapoints fetched: {(all_data)}")

Use this example to calculate IV using forward log moneyness

import http.client
import json

# Enter your Kaiko API Key
api_key = "KAIKO_API_KEY"
api_host = "us.market-api.kaiko.io"
api_base_endpoint = "/v2/data/analytics.v2/implied_volatility_smile"
# Start of mandatory parameter configuration
mandatory_params = {
    "base": "btc",
    "quote": "usd",
    "value_time": "2024-06-07T12:00:00.000Z",
    "expiry": "2024-06-28T00:00:00.000Z",
    "strikes": "30000,50000,60000,70000,90000",
}
# End of mandatory parameter configuration
# Start of optional parameter configuration
optional_params = {
    "exchanges": "drbt"
}
# End of optional parameter configuration
conn = http.client.HTTPSConnection(api_host)
headers = {
    "X-Api-Key": api_key,
    "Accept": "application/json"
}

all_params = {**mandatory_params, **optional_params}

url_params = []
for param, value in all_params.items():
    url_params.append(f"{param}={value}")
url_params = '&'.join(url_params)

endpoint_with_params = f"{api_base_endpoint}?{url_params}"
# Pagination for next pages
all_data = []
next_url = endpoint_with_params
while next_url:
    conn.request("GET", next_url, headers=headers)
    response = conn.getresponse()
    data = json.loads(response.read().decode("utf-8"))
    all_data.extend(data.get("data", []))
    print(f"Fetched {len(data.get('data', []))} datapoints. Total: {len(all_data)}")
    next_url = data.get("next_url", "").replace("https://us.market-api.kaiko.io", "")
    if not next_url:
        break
conn.close()
print(f" datapoints fetched: {(all_data)}")

Response examples

{
    "query": {
        "base": "btc",
        "quote": "usd",
        "exchanges": [
            "drbt",
            "okex"
        ],
        "value_time": "2024-06-07T12:00:00.000Z",
        "expiry": "2024-06-28T00:00:00.000Z",
        "data_version": "v2",
        "commodity": "analytics",
        "request_time": "2024-06-24T12:30:09.700Z",
        "sources": "false"
    },
    "time": "2024-06-24T12:30:10.147Z",
    "data": [
        {
            "value_time": "2024-06-07T12:00:00.000Z",
            "expiry": "2024-06-28T00:00:00.000Z",
            "time_to_expiry": 0.056164383561643834,
            "implied_volatilities": [
                {
                    "strike": 72853.3324003775,
                    "forward_log_moneyness": 0.007321081822738051,
                    "implied_volatility": 0.5105897940662363,
                    "delta": 0.5,
                    "gamma": 0.000045971145294598765,
                    "current_spot": 71717,
                    "interest_rate": 0.14954983972466698
                },
                {
                    "strike": 79392.23132701412,
                    "forward_log_moneyness": 0.09327332815155387,
                    "implied_volatility": 0.5335098490669691,
                    "delta": 0.25,
                    "gamma": 0.00003504506121504308,
                    "current_spot": 71717,
                    "interest_rate": 0.14954983972466698
                },
                {
                    "strike": 67169.33106494324,
                    "forward_log_moneyness": -0.07391043269308284,
                    "implied_volatility": 0.5076566142080143,
                    "delta": 0.75,
                    "gamma": 0.000036829787686483384,
                    "current_spot": 71717,
                    "interest_rate": 0.14954983972466698
                }
            ]
        }
    ],
    "exchanges": [
        "drbt",
        "okex"
    ]
}

{
   "query": {
      "base": "btc",
      "quote": "usd",
      "exchanges": [
         "drbt",
         "okex"
      ],
      "value_time": "2024-09-12T10:00:00.000Z",
      "expiry": "2024-09-27T08:00:00.000Z",
      "data_version": "v2",
      "commodity": "analytics",
      "request_time": "2024-09-16T10:08:13.297Z",
      "sources": "false"
   },
   "time": "2024-09-16T10:08:13.510Z",
   "data": [
      {
         "value_time": "2024-09-12T10:00:00.000Z",
         "expiry": "2024-09-27T00:00:00.000Z",
         "time_to_expiry": 0.03995433789954338,
         "implied_volatilities": [
            {
               "strike": 21393.433382294108,
               "forward_log_moneyness": -1,
               "implied_volatility": 1.333640363610205,
               "delta": 0.9999487436462999,
               "gamma": 1.3636212810241294E-8,
               "current_spot": 58033.01112255454,
               "interest_rate": 0.051859643540835755
            },
            {
               "strike": 35271.80867069449,
               "forward_log_moneyness": -0.5,
               "implied_volatility": 0.9596570717413877,
               "delta": 0.9965589532046168,
               "gamma": 9.298329941261203E-7,
               "current_spot": 58033.01112255454,
               "interest_rate": 0.051859643540835755
            },
            {
               "strike": 58153.381211439206,
               "forward_log_moneyness": 0,
               "implied_volatility": 0.5101368982713104,
               "delta": 0.5203310896967671,
               "gamma": 6.732894295644585E-5,
               "current_spot": 58033.01112255454,
               "interest_rate": 0.051859643540835755
            },
            {
               "strike": 95878.71656643301,
               "forward_log_moneyness": 0.5,
               "implied_volatility": 0.8386751286583922,
               "delta": 0.0018731164887705876,
               "gamma": 6.140349526013891E-7,
               "current_spot": 58033.01112255454,
               "interest_rate": 0.051859643540835755
            },
            {
               "strike": 158077.27941050686,
               "forward_log_moneyness": 1,
               "implied_volatility": 1.1585659255535645,
               "delta": 1.3207614779298105E-5,
               "gamma": 4.342680303635139E-9,
               "current_spot": 58033.01112255454,
               "interest_rate": 0.051859643540835755
            }
         ]
      }
   ]
}

{
   "query": {
      "base": "btc",
      "quote": "usd",
      "exchanges": [
         "drbt"
      ],
      "value_time": "2024-09-12T10:00:00.000Z",
      "expiry": "2024-09-27T08:00:00.000Z",
      "data_version": "v2",
      "commodity": "analytics",
      "request_time": "2024-09-16T10:16:06.767Z",
      "sources": "false"
   },
   "time": "2024-09-16T10:16:07.109Z",
   "data": [
      {
         "value_time": "2024-09-12T10:00:00.000Z",
         "expiry": "2024-09-27T08:00:00.000Z",
         "time_to_expiry": 0.0408675799086758,
         "implied_volatilities": [
            {
               "strike": 30000,
               "forward_log_moneyness": -0.6621439523959698,
               "implied_volatility": 1.0918347265102102,
               "delta": 0.999065374274305,
               "gamma": 2.470728795941105E-7,
               "current_spot": 58026.01780838792,
               "interest_rate": 0.0599458347465653
            },
            {
               "strike": 50000,
               "forward_log_moneyness": -0.15131832862997915,
               "implied_volatility": 0.6151097548518855,
               "delta": 0.8995619045026346,
               "gamma": 2.4400231724112595E-5,
               "current_spot": 58026.01780838792,
               "interest_rate": 0.0599458347465653
            },
            {
               "strike": 60000,
               "forward_log_moneyness": 0.031003228163975546,
               "implied_volatility": 0.5087453039141314,
               "delta": 0.40128287640417803,
               "gamma": 6.479219462479912E-5,
               "current_spot": 58026.01780838792,
               "interest_rate": 0.0599458347465653
            },
            {
               "strike": 70000,
               "forward_log_moneyness": 0.18515390799123382,
               "implied_volatility": 0.5834792805075438,
               "delta": 0.06542894780360681,
               "gamma": 1.861991887220773E-5,
               "current_spot": 58026.01780838792,
               "interest_rate": 0.0599458347465653
            },
            {
               "strike": 90000,
               "forward_log_moneyness": 0.4364683362721398,
               "implied_volatility": 0.7752384746098042,
               "delta": 0.0033982150399509137,
               "gamma": 1.125492902360329E-6,
               "current_spot": 58026.01780838792,
               "interest_rate": 0.0599458347465653
            }
         ]
      }
   ]
}
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