API — Probability density

Probability density

Breeden-Litzenberger probability density derived from option prices. Returns PDF, normalized PDF, CDF (above and below spot), and distribution stats (mean, std, mode, skew, kurtosis, 25/50/75 percentile prices) per expiry.

Filters:

expiry — slice to a single expiry token (case-insensitive).
dte_max — drop expiries with DTE > dte_max so near-term clients can avoid carrying the long tail.
confidence_band — when set to 0.68 or 0.95 (the most common choices), each expiry payload gets a confidence_band object with lower / upper price levels containing that much implied probability mass, computed by interpolating the CDF.

GET

options

probability

density

Risk-neutral PDF/CDF (per expiry)

curl --request GET \
  --url https://api.example.com/options/probability/density \
  --header 'X-API-Key: <api-key>'

{
  "data": {
    "expiries": {},
    "spot_price": 123,
    "filtered_dte_max": 123,
    "confidence_band_requested": 123
  },
  "meta": {
    "version": "<string>",
    "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
}

Risk-neutral PDF/CDF derived from option prices via Breeden-Litzenberger. Optional ?confidence_band=0.68|0.95 returns interpolated price bands per expiry.

Breeden-Litzenberger explained

Authorizations

X-API-Key

string

header

required

Your BackQuant API key (same key as v1)

Headers

X-API-Key

string | null

Query Parameters

symbol

enum<string>

default:BTCUSDT

Trading symbol: BTCUSDT, ETHUSDT, SOLUSDT, or HYPEUSDT.

Available options:

BTCUSDT,

ETHUSDT,

SOLUSDT,

HYPEUSDT

expiry

string | null

Filter to one expiry token (e.g. 28MAR25)

dte_max

integer | null

Drop expiries with DTE greater than this value.

Required range: 0 <= x <= 720

confidence_band

number | null

Confidence level for the implied price band, e.g. 0.68 for ≈1σ or 0.95 for ≈2σ. Adds confidence_band per expiry.

Required range: 0.5 <= x <= 0.999

Response

Successful Response

data

ProbabilityDensityData · object

required

Show child attributes

Documentation Index

​See also

Breeden-Litzenberger explained

Authorizations

Headers

Query Parameters

Response

See also