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://{eu/us}.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_smile

Path Parameters

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

Query 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	No	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

cURL

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

Python (Deltas)

Use this example to calculate IV using deltas

##### 1. Import dependencies #####
import requests
import pandas as pd

##### 2. Choose the value of the query's parameters #####
# ---- Required parameters ---- #
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"

# ---- Optional parameters ---- #
exchanges = "drbt"

# ---- API key configuration ---- #
api_key = "YOUR_API_KEY"

##### 3. Get the data #####
# ---- Function to run an API call ---- # 
# Get the data in a dataframe --------- # 

def get_kaiko_data(api_key: str, base: str, quote: str, value_time: str, expiry: str, deltas: str, exchanges: str = None):
    headers = {'Accept': 'application/json', 'X-Api-Key': api_key}
    
    url = f'https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_smile'
    params = {
        "base": base,
        "quote": quote,
        "value_time": value_time,
        "expiry": expiry,
        "deltas": deltas,
        "exchanges": exchanges
    }

    try:
        res = requests.get(url, headers=headers, params=params)
        res.raise_for_status() 
        data = res.json()
        if 'data' not in data:
            print("No data returned.")
            return pd.DataFrame() 
        df = pd.DataFrame(data['data'])

        # Handle pagination with continuation token
        while 'next_url' in data:
            next_url = data['next_url']
            if next_url is None:
                break
            res = requests.get(next_url, headers=headers)
            res.raise_for_status()
            data = res.json()
            if 'data' in data:
                df = pd.concat([df, pd.DataFrame(data['data'])], ignore_index=True)
        return df

    except requests.exceptions.RequestException as e:
        print(f"API request error: {e}")
        return pd.DataFrame() 

# ---- Get the data ---- #
df = get_kaiko_data(api_key=api_key, base=base, quote=quote, value_time=value_time, expiry=expiry, deltas=deltas, exchanges=exchanges)
print (df)

Python (Forward log moneyness)

Use this example to calculate IV using forward log moneyness

##### 1. Import dependencies #####
import requests
import pandas as pd

##### 2. Choose the value of the query's parameters #####
# ---- Required parameters ---- #
base = "btc"
quote = "usd"
value_time = "2022-09-20T16:15:00.000Z"
expiry = "2022-12-30T08:00:00.000Z"
forward_log_moneynesses = "-1,-0.5,0,0.5,1"

# ---- Optional parameters ---- #
exchanges = "drbt"

# ---- API key configuration ---- #
api_key = "YOUR_API_KEY"

##### 3. Get the data #####
# ---- Function to run an API call ---- # 
# Get the data in a dataframe --------- # 

def get_kaiko_data(api_key: str, base: str, quote: str, value_time: str, expiry: str, forward_log_moneynesses: str, exchanges: str = None):
    headers = {'Accept': 'application/json', 'X-Api-Key': api_key}
    
    url = f'https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_smile'
    params = {
        "base": base,
        "quote": quote,
        "value_time": value_time,
        "expiry": expiry,
        "forward_log_moneynesses": forward_log_moneynesses,
        "exchanges": exchanges
    }

    try:
        res = requests.get(url, headers=headers, params=params)
        res.raise_for_status() 
        data = res.json()
        if 'data' not in data:
            print("No data returned.")
            return pd.DataFrame() 
        df = pd.DataFrame(data['data'])

        # Handle pagination with continuation token
        while 'next_url' in data:
            next_url = data['next_url']
            if next_url is None:
                break
            res = requests.get(next_url, headers=headers)
            res.raise_for_status()
            data = res.json()
            if 'data' in data:
                df = pd.concat([df, pd.DataFrame(data['data'])], ignore_index=True)
        return df

    except requests.exceptions.RequestException as e:
        print(f"API request error: {e}")
        return pd.DataFrame() 

# ---- Get the data ---- #
df = get_kaiko_data(api_key=api_key, base=base, quote=quote, value_time=value_time, expiry=expiry, forward_log_moneynesses=forward_log_moneynesses, exchanges=exchanges)
print (df)

Python (Strikes)

Use this example to calculate IV using forward log moneyness

##### 1. Import dependencies #####
import requests
import pandas as pd

##### 2. Choose the value of the query's parameters #####
# ---- Required parameters ---- #
base = "btc"
quote = "usd"
value_time = "2022-09-20T16:15:00.000Z"
expiry = "2022-12-30T08:00:00.000Z"
strikes = "10000,15000,20000"

# ---- Optional parameters ---- #
exchanges = "drbt"

# ---- API key configuration ---- #
api_key = "YOUR_API_KEY"

##### 3. Get the data #####
# ---- Function to run an API call ---- # 
# Get the data in a dataframe --------- # 

def get_kaiko_data(api_key: str, base: str, quote: str, value_time: str, expiry: str, strikes: str, exchanges: str = None):
    headers = {'Accept': 'application/json', 'X-Api-Key': api_key}
    
    url = f'https://us.market-api.kaiko.io/v2/data/analytics.v2/implied_volatility_smile'
    params = {
        "base": base,
        "quote": quote,
        "value_time": value_time,
        "expiry": expiry,
        "strikes": strikes,
        "exchanges": exchanges
    }

    try:
        res = requests.get(url, headers=headers, params=params)
        res.raise_for_status() 
        data = res.json()
        if 'data' not in data:
            print("No data returned.")
            return pd.DataFrame() 
        df = pd.DataFrame(data['data'])

        # Handle pagination with continuation token
        while 'next_url' in data:
            next_url = data['next_url']
            if next_url is None:
                break
            res = requests.get(next_url, headers=headers)
            res.raise_for_status()
            data = res.json()
            if 'data' in data:
                df = pd.concat([df, pd.DataFrame(data['data'])], ignore_index=True)
        return df

    except requests.exceptions.RequestException as e:
        print(f"API request error: {e}")
        return pd.DataFrame() 

# ---- Get the data ---- #
df = get_kaiko_data(api_key=api_key, base=base, quote=quote, value_time=value_time, expiry=expiry, strikes=strikes, exchanges=exchanges)
print (df)

Response examples

Deltas

{
    "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"
    ]
}

Forward log moneyness

{
   "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
            }
         ]
      }
   ]
}

Strikes

{
   "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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