---
title: "Risk-neutral PDF/CDF (per expiry)"
method: GET
path: "/options/probability/density"
tags: ["Options"]
---

# Risk-neutral PDF/CDF (per expiry)

`GET /options/probability/density`

## Request

- Base URL: `https://docs.backquant.com/v2`
- URL: `https://docs.backquant.com/v2/options/probability/density`
- Auth: API key in header `X-API-Key`

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.

## Query parameters

- `symbol` 'BTCUSDT' | 'ETHUSDT' | 'SOLUSDT' | 'HYPEUSDT': Trading symbol: BTCUSDT, ETHUSDT, SOLUSDT, or HYPEUSDT.
- `expiry` string, nullable: Filter to one expiry token (e.g. 28MAR25)
- `dte_max` integer, nullable: Drop expiries with DTE greater than this value.
- `confidence_band` number, nullable: Confidence level for the implied price band, e.g. `0.68` for ≈1σ or `0.95` for ≈2σ. Adds `confidence_band` per expiry.

## Headers

- `X-API-Key` string, nullable

## Response `200`

Successful Response

- ProbabilityDensityResponse
  - `success` true
  - `data` ProbabilityDensityData, required
    - `expiries` object, required: Keyed by expiry token (e.g. `28MAR25`).
    - `spot_price` number, nullable
    - `filtered_dte_max` integer, nullable
    - `confidence_band_requested` number, nullable
  - `meta` V2Meta, required: 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`.
    - `version` '2.0', required: API version tag.
    - `timestamp` string, required: ISO 8601 wall-clock when the response was built.
    - `request_id` string, nullable: X-Request-ID for tracing across logs / Sentry.
    - `symbol` string, nullable: Symbol the response is about, if applicable.
    - `spot_price` number, nullable: Current spot price for the symbol.
    - `computed_at` string, nullable: ISO 8601 of when the underlying cache value was last written.
    - `freshness_seconds` number, nullable: `now - computed_at` in seconds; useful for staleness alarms.
    - `source` string[], nullable: Upstream venue list the data flowed through.
    - `exchanges_filtered` string[], nullable: Echo of the `?exchanges=` filter when one was applied.
    - `rate_limit` object, nullable: `{limit, remaining, reset}` echo of the rate-limit headers.
    - `extra` object, nullable: Open dict for endpoint-specific metadata (filter_hash, etc.).

## Other responses

- `401`: Invalid or missing API key
- `404`: Not Found
- `422`: Validation error on query parameters
- `429`: Rate limit exceeded

---

[API](https://skmtc.dev/backquant/apis/backquant-api-v2.md) · [All operations](https://skmtc.dev/backquant/apis/backquant-api-v2/llms.txt) · [OpenAPI document](https://skmtc.dev/backquant/apis/backquant-api-v2/revisions/3c1c96b3cc24?raw)