Risk Neutral Density

Family: Volatility

What it computes

Emits RiskNeutralDensityTick ticks carrying per_strike density, integrated_mass off chain snapshot.

Available on the live and replay drives. The historical drive fails closed with KAIROS_ERR_HISTORICAL_UNWIRED until the relevant cache is hydrated externally.

Methodology

Breeden-Litzenberger (1978) q(K) = e^{rT} * d²C/dK² density via the three-point non-uniform-grid stencil on the listed call-mid strip (exact for quadratics on any strike spacing).

See the methodology overview for the citation index.

Inputs

Chain snapshot.

Key outputs

Per_strike density, integrated_mass. The full field set is in the tick table below.

Output schema (RiskNeutralDensityTick)

The field / type / description table below is regenerated from the RiskNeutralDensityTick Rust source by docs-site/scripts/inject-doc-tables.ts on every npm run docs:build. Do not hand-edit between the sentinels.

Field	Type	Description
symbol	Arc<str>	Underlying symbol (interned).
date	i32	Trading-session date (YYYYMMDD) at emission time.
ms_of_day	i32	Milliseconds since midnight at emission time.
expiration	i32	Expiration YYYYMMDD for which the density was recovered.
strikes_used	i32	Count of interior strikes the second-difference admitted.
integrated_mass	f64	Total mass: trapezoidal integral of the recovered density over the admitted strike grid. A well-formed density integrates to approximately 1.0; deviations flag a sparse or arbitraged strip.
per_strike	Vec<DensityPoint>	Per-strike density points, oldest-strike first.

Configuration (RiskNeutralDensityParams)

Regenerated from the RiskNeutralDensityParams Rust source — see the note above.

Field	Type	Description
contracts	SecurityFilter	Underlying symbols the subscription tracks.
conditions	ConditionPolicy	Trade-condition admission policy. Retained for surface consistency with the other vol analytics; the density kernel operates on the chain snapshot, not the live trade tape.
venues	ExchangeFilter	Exchange / venue admission policy. Retained for surface consistency with the other vol analytics.
daily_close	Arc<DailyCloseCache>	Boot-time hydrated daily-close history. The empty default is a placeholder — the analytic's per-strike density kernel consumes a chain snapshot rather than the daily-close history, but the cache slot is retained so the DefaultSpec hook can fail closed with the same documented cache-dependency error the other vol analytics surface.
min_strikes	i32	Minimum number of admitted strikes for the centred second-difference. Defaults to [DEFAULT_MIN_STRIKES] (5).
risk_free_rate	f64	Risk-free rate (annualised continuously compounded) for the e^{rT} discount unwind on the second derivative. 0.0 selects the institutional default of r = 0 — sufficient for the short-tenor equity-options regime where the per-tenor r·T factor is small.
target_expiration	i32	Target expiration YYYYMMDD. 0 selects the front expiration on the supplied chain snapshot (the per-symbol nearest-dated expiration with at least min_strikes admitted strikes).

Example

Python

import kairos_thetadata as kt

client = kt.Client.connect(kt.Credentials.from_env())

def on_event(row):
    print(row)

sub = client.live().risk_neutral_density(["SPX"]).on_event(on_event)
sub.wait(timeout_seconds=60.0)

TypeScript

import { Client, Credentials } from "kairos-thetadata";

const client = await Client.connect(Credentials.fromEnv());

await client
  .live()
  .riskNeutralDensity(["SPX"])
  .onEvent((tick) => {
    console.log(tick);
  });

Rust

// Cargo.toml:
//   kairos = "0.1"

use kairos::{Client, RiskNeutralDensityRow};

# fn run() -> Result<(), Box<dyn std::error::Error>> {
let client = Client::connect(("me@example.com", "secret"))?;

let sub = client
    .live()
    .risk_neutral_density(["SPX"])
    .on_event(|row: &RiskNeutralDensityRow| println!("strikes_used={} integrated_mass={}", row.strikes_used, row.integrated_mass))?;
// ... later ...
sub.unsubscribe();
# Ok(())
# }