Butterfly Arb Residual

Family: Stat-arb

What it computes

Emits ButterflyArbResidualTick ticks carrying strikes_used, violations, min_residual, per_strike (strike, residual_value, residual_pct) 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

Carr-Madan (2001) discrete butterfly no-arbitrage residual C(K-h) − 2·C(K) + C(K+h) at every interior strike on the listed call-mid strip — chain-convexity screen the desk runs before the Breeden-Litzenberger density recovery.

See the methodology overview for the citation index.

Inputs

Chain snapshot.

Key outputs

Strikes_used, violations, min_residual, per_strike (strike, residual_value, residual_pct). The full field set is in the tick table below.

Output schema (ButterflyArbResidualTick)

The field / type / description table below is regenerated from the ButterflyArbResidualTick 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 residuals were recovered.
strikes_used	i32	Count of interior strikes the residual sweep admitted.
violations	i32	Count of admitted interior strikes whose residual is strictly negative — the chain's butterfly-arbitrage violation count.
min_residual	f64	Minimum recovered residual across the admitted interior strikes; negative values flag a butterfly violation.
per_strike	Vec<ButterflyResidualPoint>	Per-strike residual points, oldest-strike first.

Configuration (ButterflyArbResidualParams)

Regenerated from the ButterflyArbResidualParams 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 no-arbitrage analytics; the residual kernel operates on the chain snapshot, not the live trade tape.
venues	ExchangeFilter	Exchange / venue admission policy. Retained for surface consistency with the other no-arbitrage analytics.
daily_close	Arc<DailyCloseCache>	Boot-time hydrated daily-close history. The empty default is a placeholder — the 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 chain-driven analytics surface.
min_strikes	i32	Minimum number of admitted strikes for the residual sweep. Defaults to [DEFAULT_MIN_STRIKES] (3).
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().butterfly_arb_residual(["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()
  .butterflyArbResidual(["SPX"])
  .onEvent((tick) => {
    console.log(tick);
  });

Rust

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

use kairos::{Client, ButterflyArbResidualRow};

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

let sub = client
    .live()
    .butterfly_arb_residual(["SPX"])
    .on_event(|row: &ButterflyArbResidualRow| {
        println!("min_residual={} violations={}", row.min_residual, row.violations)
    })?;
// ... later ...
sub.unsubscribe();
# Ok(())
# }