Probability density
Risk-neutral PDF/CDF (per expiry). Breeden-Litzenberger probability density derived from option prices.
curl --request GET \
--url https://api.example.com/options/probability/density \
--header 'X-API-Key: <api-key>'import requests
url = "https://api.example.com/options/probability/density"
headers = {"X-API-Key": "<api-key>"}
response = requests.get(url, headers=headers)
print(response.text)const options = {method: 'GET', headers: {'X-API-Key': '<api-key>'}};
fetch('https://api.example.com/options/probability/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.example.com/options/probability/density",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "GET",
CURLOPT_HTTPHEADER => [
"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"
"net/http"
"io"
)
func main() {
url := "https://api.example.com/options/probability/density"
req, _ := http.NewRequest("GET", url, nil)
req.Header.Add("X-API-Key", "<api-key>")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.get("https://api.example.com/options/probability/density")
.header("X-API-Key", "<api-key>")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.example.com/options/probability/density")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Get.new(url)
request["X-API-Key"] = '<api-key>'
response = http.request(request)
puts response.read_body{
"data": {
"expiries": {},
"spot_price": 123,
"filtered_dte_max": 123,
"confidence_band_requested": 123
},
"meta": {
"version": "2.0",
"timestamp": "<string>",
"request_id": "<string>",
"symbol": "<string>",
"spot_price": 123,
"computed_at": "<string>",
"freshness_seconds": 123,
"source": [
"<string>"
],
"exchanges_filtered": [
"<string>"
],
"rate_limit": {},
"extra": {}
},
"success": true
}{
"success": false,
"error": {
"code": "UNAUTHORIZED",
"message": "Invalid API key"
},
"meta": {
"version": "2.0",
"timestamp": "2026-04-29T12:00:00Z"
}
}{
"error": {
"code": "<string>",
"message": "<string>",
"details": {}
},
"meta": {
"version": "2.0",
"timestamp": "<string>",
"request_id": "<string>",
"symbol": "<string>",
"spot_price": 123,
"computed_at": "<string>",
"freshness_seconds": 123,
"source": [
"<string>"
],
"exchanges_filtered": [
"<string>"
],
"rate_limit": {},
"extra": {}
},
"success": false
}{
"success": false,
"error": {
"code": "VALIDATION_ERROR",
"message": "Invalid request parameters",
"details": {
"errors": []
}
},
"meta": {
"version": "2.0",
"timestamp": "2026-04-29T12:00:00Z"
}
}{
"success": false,
"error": {
"code": "RATE_LIMIT_EXCEEDED",
"message": "Rate limit exceeded. Try again later."
},
"meta": {
"version": "2.0",
"timestamp": "2026-04-29T12:00:00Z"
}
}?confidence_band=0.68|0.95 returns interpolated price bands per expiry.
See also
Breeden-Litzenberger explained
Authorizations
Your BackQuant API key (same key as v1)
Headers
Query Parameters
Trading symbol: BTCUSDT, ETHUSDT, SOLUSDT, or HYPEUSDT.
BTCUSDT, ETHUSDT, SOLUSDT, HYPEUSDT Filter to one expiry token (e.g. 28MAR25)
Drop expiries with DTE greater than this value.
0 <= x <= 720Confidence level for the implied price band, e.g. 0.68 for ≈1σ or 0.95 for ≈2σ. Adds confidence_band per expiry.
0.5 <= x <= 0.999Response
Successful Response
Show child attributes
Show child attributes
The meta block returned alongside every v2 response.
Every field after version/timestamp is optional because endpoints
attach different combinations - e.g. /v2/status skips symbol, the
chain endpoint sets extra.filter_hash, etc. Listing them here means
SDKs get a typed accessor for each instead of a generic meta: dict.
Show child attributes
Show child attributes
curl --request GET \
--url https://api.example.com/options/probability/density \
--header 'X-API-Key: <api-key>'import requests
url = "https://api.example.com/options/probability/density"
headers = {"X-API-Key": "<api-key>"}
response = requests.get(url, headers=headers)
print(response.text)const options = {method: 'GET', headers: {'X-API-Key': '<api-key>'}};
fetch('https://api.example.com/options/probability/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.example.com/options/probability/density",
CURLOPT_RETURNTRANSFER => true,
CURLOPT_ENCODING => "",
CURLOPT_MAXREDIRS => 10,
CURLOPT_TIMEOUT => 30,
CURLOPT_HTTP_VERSION => CURL_HTTP_VERSION_1_1,
CURLOPT_CUSTOMREQUEST => "GET",
CURLOPT_HTTPHEADER => [
"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"
"net/http"
"io"
)
func main() {
url := "https://api.example.com/options/probability/density"
req, _ := http.NewRequest("GET", url, nil)
req.Header.Add("X-API-Key", "<api-key>")
res, _ := http.DefaultClient.Do(req)
defer res.Body.Close()
body, _ := io.ReadAll(res.Body)
fmt.Println(string(body))
}HttpResponse<String> response = Unirest.get("https://api.example.com/options/probability/density")
.header("X-API-Key", "<api-key>")
.asString();require 'uri'
require 'net/http'
url = URI("https://api.example.com/options/probability/density")
http = Net::HTTP.new(url.host, url.port)
http.use_ssl = true
request = Net::HTTP::Get.new(url)
request["X-API-Key"] = '<api-key>'
response = http.request(request)
puts response.read_body{
"data": {
"expiries": {},
"spot_price": 123,
"filtered_dte_max": 123,
"confidence_band_requested": 123
},
"meta": {
"version": "2.0",
"timestamp": "<string>",
"request_id": "<string>",
"symbol": "<string>",
"spot_price": 123,
"computed_at": "<string>",
"freshness_seconds": 123,
"source": [
"<string>"
],
"exchanges_filtered": [
"<string>"
],
"rate_limit": {},
"extra": {}
},
"success": true
}{
"success": false,
"error": {
"code": "UNAUTHORIZED",
"message": "Invalid API key"
},
"meta": {
"version": "2.0",
"timestamp": "2026-04-29T12:00:00Z"
}
}{
"error": {
"code": "<string>",
"message": "<string>",
"details": {}
},
"meta": {
"version": "2.0",
"timestamp": "<string>",
"request_id": "<string>",
"symbol": "<string>",
"spot_price": 123,
"computed_at": "<string>",
"freshness_seconds": 123,
"source": [
"<string>"
],
"exchanges_filtered": [
"<string>"
],
"rate_limit": {},
"extra": {}
},
"success": false
}{
"success": false,
"error": {
"code": "VALIDATION_ERROR",
"message": "Invalid request parameters",
"details": {
"errors": []
}
},
"meta": {
"version": "2.0",
"timestamp": "2026-04-29T12:00:00Z"
}
}{
"success": false,
"error": {
"code": "RATE_LIMIT_EXCEEDED",
"message": "Rate limit exceeded. Try again later."
},
"meta": {
"version": "2.0",
"timestamp": "2026-04-29T12:00:00Z"
}
}