VolFoundry
volatility infrastructure
open-source volatility infrastructure
VolFoundry inverts live Deribit quotes through Black-76, extracts a forward per expiry, fits raw-SVI smiles and a global SSVI surface, then reports static-arbitrage diagnostics with their evaluation domain and tolerance. Everything below this line is running on live market data, in this browser tab — no server, no replay.
Methodology
The pipeline that turns a raw quote into a validated surface, with each step tied to its
source in the literature and to where it runs in the code. Conventions: volatility is decimal
(0.60 = 60%), maturity \(T\) is in years on ACT/365, log-moneyness is \(k=\ln(K/F)\), and
total variance is \(w(k,T)=\sigma^2(k,T)\,T\). Full derivations are in the repository under
docs/derivations/; numbered references are listed below.
Black's forward measure [1]: crypto options settle
against a future, so the forward — not spot — is the state variable.
In VolFoundry: pricers.black76_price evaluates this; iv.implied_volatility
inverts it for \(\sigma\) by Newton on vega with a bracketed (Brent) fallback, holding the root
in \(\sigma\in(0,5]\).
A model-free identity. Regressing \(C-P\) on \(K\) across paired strikes yields
slope \(-e^{-rT}\), hence the discount factor and forward, per expiry — no constant-rate or
zero-basis assumption. In VolFoundry: SurfaceBuilder runs this regression;
the live panels above use Deribit's per-expiry underlying_price as \(F\).
Gatheral's stochastic-volatility-inspired form [3];
its wing slopes \(b(1\pm\rho)\) obey Lee's moment bound \(\le 2\) [5].
In VolFoundry: svi.calibrate_svi_slice uses the Zeliade quasi-explicit scheme
[6] — outer search over \((m,\sigma)\), inner constrained
least-squares for \((a,b,\rho)\).
Non-negative risk-neutral density in Gatheral–Jacquier form [4],
cross-checked against the Breeden–Litzenberger density \(\partial^2C/\partial K^2\ge 0\)
[2]. In VolFoundry: arbitrage evaluates \(g(k)\)
over a stated domain (e.g. \(k\in[-2,2]\), 1001 pts) at a reported tolerance — evidence over that
grid, not a proof over the whole real line.
SSVI couples the slices through ATM total variance \(\theta(T)\) and a \(\varphi(\theta)\) family; Gatheral–Jacquier give the parameter conditions for a calendar- and butterfly-free surface [4]. In VolFoundry: strict validation enforces these during calibration and rejects violating fits, rather than auditing after the fact.
Zero-bid, crossed and stale quotes, sub-day maturities and prices outside the
static no-arbitrage bounds are removed before inversion. In VolFoundry: the
data layer records per-reason drop counts so the surface is auditable — a fit is
only as sound as the quotes beneath it.
Pure Python, typed, tested against analytic cases and reference surfaces. Same code path the panels on this page are modelled on.
# install $ pip install volfoundry # live chain → calibrated, validated surface $ volfoundry live --currency BTC --out surface.json # or from Python >>> from volfoundry import Chain, SSVISurface >>> chain = Chain.from_deribit("BTC") >>> surface = SSVISurface.calibrate(chain) >>> surface.validate(domain=(-2, 2), n=1001).is_valid True >>> surface.iv(k=0.0, T=30/365) 0.5812
mark_iv, not an executable price. Numerical no-arbitrage checks are
reported together with their evaluation domain, grid and tolerance and are not a guarantee of
arbitrage-freeness over all strikes and maturities. Validate independently before any
financial use.