hagan-sabr

The SABR stochastic-volatility model — the Hagan et al. (2002) implied-volatility expansions (lognormal and normal), the Obłój correction, and (α, ρ, ν) calibration to a market smile. Zero dependencies.

npm install hagan-sabr

Why

SABR is the market-standard model for interest-rate swaption and FX volatility smiles — but there was no focused JavaScript/TypeScript implementation. @quantlib/ql has it buried in a 28 MB WASM bundle behind a C++-style API. This is the Hagan formulas as a handful of typed functions, and its lognormal output matches QuantLib's sabrVolatility to 1e-9 across 315 test cases.

import { lognormalVol, calibrate } from "hagan-sabr";

const p = { alpha: 0.2, beta: 0.5, rho: -0.3, nu: 0.4 };
lognormalVol(100, 100, 1, p);   // ATM Black vol ≈ 0.0202
lognormalVol(100, 80, 1, p);    // the smile at a lower strike

// Fit (α, ρ, ν) to a market smile (β fixed):
const fit = calibrate(100, 2, [
  { strike: 80, vol: 0.245 },
  { strike: 100, vol: 0.202 },
  { strike: 120, vol: 0.199 },
  // …
], { beta: 0.5 });
fit.alpha; fit.rho; fit.nu; fit.rmse;

API

Parameters: forward F, strike K, expiry T (years), and { alpha, beta, rho, nu } — α > 0, 0 ≤ β ≤ 1, −1 < ρ < 1, ν ≥ 0. Vols are decimals.

• lognormalVol(F, K, T, params) — Hagan Black/lognormal implied vol (matches QuantLib).
• normalVol(F, K, T, params) — Hagan Bachelier/normal implied vol (eq. 2.18).
• oblojVol(F, K, T, params) — the Obłój (2008) refinement that fixes the small-strike / long-maturity leading term.
• calibrate(F, T, quotes, opts?) — least-squares fit of (α, ρ, ν) with β fixed (default 0.5), via Nelder–Mead; returns the params plus fit rmse.

Invalid inputs throw RangeError.

Correctness

The lognormal expansion is validated against QuantLib's sabrVolatility — 315 fixtures spanning β ∈ {0, 0.3, 0.5, 0.7, 1}, forwards from 0.02 to 100, expiries to 5y, and strikes from deep ITM to deep OTM — all matching to 1e-9 (test/generate-fixtures.py). The normal and Obłój variants are cross-checked against an independent reference implementation, and calibration is verified to recover known parameters from a synthetic smile.

Related

Pairs with svi-vol-surface (arbitrage-free surface parametrization). Part of a quant/fixed-income toolkit: compounded-sofr · day-count · instrument-identifiers · newyorkfed.

Author

Built by Moshe Malka — engineering leader in New York City. Studio work at Quentin.Code.

MIT © Moshe Malka