SABR Probability Density
curl --request POST \
--url https://api.fincept.in/quantlib/volatility/sabr/density \
--header 'Content-Type: application/json' \
--header 'X-API-Key: <api-key>' \
--data '
{
"forward": 100,
"expiry": 1,
"alpha": 0.25,
"beta": 0.5,
"rho": -0.2,
"nu": 0.3,
"strikes": [
85,
90,
95,
100,
105,
110,
115
]
}
'import requests
url = "https://api.fincept.in/quantlib/volatility/sabr/density"
payload = {
"forward": 100,
"expiry": 1,
"alpha": 0.25,
"beta": 0.5,
"rho": -0.2,
"nu": 0.3,
"strikes": [85, 90, 95, 100, 105, 110, 115]
}
headers = {
"X-API-Key": "<api-key>",
"Content-Type": "application/json"
}
response = requests.post(url, json=payload, headers=headers)
print(response.text)const options = {
method: 'POST',
headers: {'X-API-Key': '<api-key>', 'Content-Type': 'application/json'},
body: JSON.stringify({
forward: 100,
expiry: 1,
alpha: 0.25,
beta: 0.5,
rho: -0.2,
nu: 0.3,
strikes: [85, 90, 95, 100, 105, 110, 115]
})
};
fetch('https://api.fincept.in/quantlib/volatility/sabr/density', options)
.then(res => res.json())
.then(res => console.log(res))
.catch(err => console.error(err));<?php
$curl = curl_init();
curl_setopt_array($curl, [
CURLOPT_URL => "https://api.fincept.in/quantlib/volatility/sabr/density",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "POST",
CURLOPT_POSTFIELDS => json_encode([
'forward' => 100,
'expiry' => 1,
'alpha' => 0.25,
'beta' => 0.5,
'rho' => -0.2,
'nu' => 0.3,
'strikes' => [
85,
90,
95,
100,
105,
110,
115
]
]),
CURLOPT_HTTPHEADER => [
"Content-Type: application/json",
"X-API-Key: <api-key>"
],
]);
$response = curl_exec($curl);
$err = curl_error($curl);
curl_close($curl);
if ($err) {
echo "cURL Error #:" . $err;
} else {
echo $response;
}package main
import (
"fmt"
"strings"
"net/http"
"io"
)
func main() {
url := "https://api.fincept.in/quantlib/volatility/sabr/density"
payload := strings.NewReader("{\n \"forward\": 100,\n \"expiry\": 1,\n \"alpha\": 0.25,\n \"beta\": 0.5,\n \"rho\": -0.2,\n \"nu\": 0.3,\n \"strikes\": [\n 85,\n 90,\n 95,\n 100,\n 105,\n 110,\n 115\n ]\n}")
req, _ := http.NewRequest("POST", url, payload)
req.Header.Add("X-API-Key", "<api-key>")
req.Header.Add("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.post("https://api.fincept.in/quantlib/volatility/sabr/density")
.header("X-API-Key", "<api-key>")
.header("Content-Type", "application/json")
.body("{\n \"forward\": 100,\n \"expiry\": 1,\n \"alpha\": 0.25,\n \"beta\": 0.5,\n \"rho\": -0.2,\n \"nu\": 0.3,\n \"strikes\": [\n 85,\n 90,\n 95,\n 100,\n 105,\n 110,\n 115\n ]\n}")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.fincept.in/quantlib/volatility/sabr/density")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Post.new(url)
request["X-API-Key"] = '<api-key>'
request["Content-Type"] = 'application/json'
request.body = "{\n \"forward\": 100,\n \"expiry\": 1,\n \"alpha\": 0.25,\n \"beta\": 0.5,\n \"rho\": -0.2,\n \"nu\": 0.3,\n \"strikes\": [\n 85,\n 90,\n 95,\n 100,\n 105,\n 110,\n 115\n ]\n}"
response = http.request(request)
puts response.read_body{
"success": true,
"data": {
"forward": 100,
"expiry": 1,
"density": [
{
"strike": 85,
"density": 0.0052
},
{
"strike": 90,
"density": 0.0118
},
{
"strike": 95,
"density": 0.0215
},
{
"strike": 100,
"density": 0.0285
},
{
"strike": 105,
"density": 0.0241
},
{
"strike": 110,
"density": 0.0152
},
{
"strike": 115,
"density": 0.0078
}
]
}
}{
"detail": "Invalid API key"
}{
"detail": "Endpoint requires Standard tier or higher"
}{
"detail": [
{
"loc": [
"body",
"volatility"
],
"msg": "field required",
"type": "value_error.missing"
}
]
}quantlib-volatility
SABR Probability Density
Calculate the risk-neutral probability density function implied by SABR parameters across multiple strike levels. Derived from the second derivative of call prices with respect to strike. Used for understanding market-implied distributions, calculating probabilities, and ensuring arbitrage-free surfaces. [Tier: PRO, Credits: 5]
POST
/
quantlib
/
volatility
/
sabr
/
density
SABR Probability Density
curl --request POST \
--url https://api.fincept.in/quantlib/volatility/sabr/density \
--header 'Content-Type: application/json' \
--header 'X-API-Key: <api-key>' \
--data '
{
"forward": 100,
"expiry": 1,
"alpha": 0.25,
"beta": 0.5,
"rho": -0.2,
"nu": 0.3,
"strikes": [
85,
90,
95,
100,
105,
110,
115
]
}
'import requests
url = "https://api.fincept.in/quantlib/volatility/sabr/density"
payload = {
"forward": 100,
"expiry": 1,
"alpha": 0.25,
"beta": 0.5,
"rho": -0.2,
"nu": 0.3,
"strikes": [85, 90, 95, 100, 105, 110, 115]
}
headers = {
"X-API-Key": "<api-key>",
"Content-Type": "application/json"
}
response = requests.post(url, json=payload, headers=headers)
print(response.text)const options = {
method: 'POST',
headers: {'X-API-Key': '<api-key>', 'Content-Type': 'application/json'},
body: JSON.stringify({
forward: 100,
expiry: 1,
alpha: 0.25,
beta: 0.5,
rho: -0.2,
nu: 0.3,
strikes: [85, 90, 95, 100, 105, 110, 115]
})
};
fetch('https://api.fincept.in/quantlib/volatility/sabr/density', options)
.then(res => res.json())
.then(res => console.log(res))
.catch(err => console.error(err));<?php
$curl = curl_init();
curl_setopt_array($curl, [
CURLOPT_URL => "https://api.fincept.in/quantlib/volatility/sabr/density",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "POST",
CURLOPT_POSTFIELDS => json_encode([
'forward' => 100,
'expiry' => 1,
'alpha' => 0.25,
'beta' => 0.5,
'rho' => -0.2,
'nu' => 0.3,
'strikes' => [
85,
90,
95,
100,
105,
110,
115
]
]),
CURLOPT_HTTPHEADER => [
"Content-Type: application/json",
"X-API-Key: <api-key>"
],
]);
$response = curl_exec($curl);
$err = curl_error($curl);
curl_close($curl);
if ($err) {
echo "cURL Error #:" . $err;
} else {
echo $response;
}package main
import (
"fmt"
"strings"
"net/http"
"io"
)
func main() {
url := "https://api.fincept.in/quantlib/volatility/sabr/density"
payload := strings.NewReader("{\n \"forward\": 100,\n \"expiry\": 1,\n \"alpha\": 0.25,\n \"beta\": 0.5,\n \"rho\": -0.2,\n \"nu\": 0.3,\n \"strikes\": [\n 85,\n 90,\n 95,\n 100,\n 105,\n 110,\n 115\n ]\n}")
req, _ := http.NewRequest("POST", url, payload)
req.Header.Add("X-API-Key", "<api-key>")
req.Header.Add("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.post("https://api.fincept.in/quantlib/volatility/sabr/density")
.header("X-API-Key", "<api-key>")
.header("Content-Type", "application/json")
.body("{\n \"forward\": 100,\n \"expiry\": 1,\n \"alpha\": 0.25,\n \"beta\": 0.5,\n \"rho\": -0.2,\n \"nu\": 0.3,\n \"strikes\": [\n 85,\n 90,\n 95,\n 100,\n 105,\n 110,\n 115\n ]\n}")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.fincept.in/quantlib/volatility/sabr/density")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Post.new(url)
request["X-API-Key"] = '<api-key>'
request["Content-Type"] = 'application/json'
request.body = "{\n \"forward\": 100,\n \"expiry\": 1,\n \"alpha\": 0.25,\n \"beta\": 0.5,\n \"rho\": -0.2,\n \"nu\": 0.3,\n \"strikes\": [\n 85,\n 90,\n 95,\n 100,\n 105,\n 110,\n 115\n ]\n}"
response = http.request(request)
puts response.read_body{
"success": true,
"data": {
"forward": 100,
"expiry": 1,
"density": [
{
"strike": 85,
"density": 0.0052
},
{
"strike": 90,
"density": 0.0118
},
{
"strike": 95,
"density": 0.0215
},
{
"strike": 100,
"density": 0.0285
},
{
"strike": 105,
"density": 0.0241
},
{
"strike": 110,
"density": 0.0152
},
{
"strike": 115,
"density": 0.0078
}
]
}
}{
"detail": "Invalid API key"
}{
"detail": "Endpoint requires Standard tier or higher"
}{
"detail": [
{
"loc": [
"body",
"volatility"
],
"msg": "field required",
"type": "value_error.missing"
}
]
}Authorizations
API key for authentication. Get your key at https://api.fincept.in/auth/register
Body
application/json
Forward price of the underlying
Required range:
x >= 0Example:
100
Time to expiry in years
Required range:
x >= 0Example:
1
SABR alpha parameter
Required range:
x >= 0Example:
0.25
SABR beta parameter
Required range:
0 <= x <= 1Example:
0.5
SABR rho parameter
Required range:
-1 <= x <= 1Example:
-0.2
SABR nu parameter
Required range:
x >= 0Example:
0.3
Array of strike prices for density evaluation
Minimum array length:
3Example:
[85, 90, 95, 100, 105, 110, 115]
⌘I
