svi-vol-surface

Gatheral's SVI implied-volatility surface — the raw / natural / jump-wings parametrizations, total implied variance, butterfly & calendar arbitrage checks, and smile calibration. Zero dependencies.

npm install svi-vol-surface

Why

SVI is the standard parametric form for an equity implied-volatility smile, and the reason it's used is that its no-arbitrage conditions are known in closed form (Gatheral & Jacquier, 2014). npm had no SVI implementation at all. This one parametrizes a slice, converts between the three standard forms, checks both static (butterfly) and calendar arbitrage, and calibrates to market quotes.

import { totalVariance, checkButterfly, calibrateRaw } from "svi-vol-surface";

const slice = { a: 0.04, b: 0.1, rho: -0.3, m: 0, sigma: 0.2 };
totalVariance(slice, 0.1);        // w(k) = σ²·t at log-moneyness 0.1

checkButterfly(slice).arbitrageFree; // true — g(k) ≥ 0 everywhere

// Fit a slice to a market smile (total-variance quotes):
const fit = calibrateRaw(quotes);
fit.rmse; fit.butterflyFree;

API

Log-moneyness k = ln(K/F); a slice returns total implied variance w(k) = σ_BS(k)²·t.

• totalVariance(raw, k) — a + b(ρ(k−m) + √((k−m)² + σ²)); impliedVol(raw, k, t) = √(w/t).
• dTotalVariance, d2TotalVariance — analytic w′(k), w″(k).
• durrlemanG(raw, k) — Durrleman's butterfly function (≥ 0 everywhere ⇔ no static arbitrage).
• checkButterfly(raw) — scans g(k) and the wing condition b(1+|ρ|) ≤ 4.
• checkCalendar(near, far) — total variance non-decreasing in maturity.
• rawToNatural / naturalToRaw / rawToJumpWings — the three parametrizations.
• calibrateRaw(quotes, opts?) — least-squares fit (Nelder–Mead) of a raw slice; returns params + rmse + butterflyFree.

Invalid parameters (b < 0, |ρ| ≥ 1, σ ≤ 0) throw RangeError.

Correctness

The static-arbitrage check is validated against the Axel Vogt parameters from Gatheral & Jacquier (2014) — a published example that does contain butterfly arbitrage — which checkButterfly correctly flags (g(k) < 0), while a clean slice passes. Analytic derivatives are checked against finite differences, parametrization conversions round-trip, and calibration recovers known parameters from a synthetic smile.

Related

Pairs with hagan-sabr (the SABR smile model). Part of a quant/fixed-income toolkit: compounded-sofr · day-count · instrument-identifiers.

Author

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

MIT © Moshe Malka