RK-SAVR estimator
Two-sample Kolmogorov–Smirnov distance on rescaled increments, with block-permuted subsampling for variance reduction.
Rough-Volatility AnalyticsarXivv2.1 · September 2026
Measure the roughness of volatility.
The first production-grade JavaScript estimator for the Hurst parameter — built on the RK-SAVR algorithm. Zero runtime dependencies, runs anywhere JavaScript runs.
MIT licensedZero runtime dependenciesNode 24+ · modern browsersESM + CJS + IIFE
RK-SAVR · live
K = 16 iterW = 2000a₁ = 1 · a₂ = 25
A note on provenance
Implementation of a peer-reviewed algorithm.
hurstify is an independent implementation of the RK-SAVR algorithm described in Angelini & Bianchi (2025), *Randomized Kolmogorov-Smirnov Analysis of Volatility Roughness*. The estimator is reproducible, deterministic given a seed, and ships with statistical inference and full model zoo.
Angelini & Bianchi (2025) — arXiv:2509.20015v3Open access · Replicated in this implementation
Read the paperWhy hurstify
One call. One number. Total clarity.
Everything you need to estimate H on real log-volatility series — packaged in a single, dependency-free module.
Multi-scale analysis
Compare rescaled distributions across arbitrary scales and weights. Single-shot, rolling, or batch.
Statistical inference
Asymptotic variance (Prop 2.9), bootstrap CIs, KS significance testing, Kalman smoothing, CUSUM break detection.
Rough-vol model zoo
rBergomi, rFSV, fOU and mPRE simulators. Hosking fBm/fGn generators and noise-correction primitives.
Pluggable optimizers
Brent, Nelder-Mead, simulated annealing, differential evolution, and adaptive grid search — pick what fits the surface.
Engineered to ship
Pure ESM + CJS + IIFE bundles, TypeScript declarations, zero runtime dependencies, Node 24+ and evergreen browsers.
A working tool, not a slide deck
Bring the estimator into your workflow.
Run the full RK-SAVR pipeline from a single call. Stream results into your dashboard, surface diagnostics in research notes, or batch across thousands of synthetic paths.
- Ĥ0.107true 0.100 · bias 0.018
- D0.0412KS distance
- 95% CI[0.08, 0.13]bootstrap
- p < 0.01truesignificant
estimator.ts
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import {Hurstify, generateFractionalBrownianMotion} from 'hurstify'; // Generate a synthetic rough-volatility path with true H = 0.10const path = generateFractionalBrownianMotion(2000, 0.10); const r = new Hurstify({ scaleA1: 1, scaleA2: 25, sampleSize: 500, iterations: 16,}); const {H, d, ci, significant} = r.estimateSingleWithDiagnostics(path); console.log(`Ĥ = ${H.toFixed(3)} true H = 0.100`);console.log(`D = ${d.toFixed(4)} CI [${ci[0].toFixed(2)}, ${ci[1].toFixed(2)}]`);console.log(`Significant at 5%: ${significant}`);
run · 1 estimator · 2000 samples · K=16
RK-SAVR · live
K = 16 iterW = 2000a₁ = 1 · a₂ = 25
How it works
A seven-step pipeline to a single number.
RK-SAVR is a randomized Kolmogorov–Smirnov estimator built around the rescaling invariance of fractional Gaussian processes. Each step isolates one source of bias.
- step 01
Segmentation
Slice the stationary window into overlapping segments long enough to resolve the slowest scale.
- step 02
Increments
Compute Z_{t,a} = X_{t+a} − X_t across scales a₁, a₂ (or a user-supplied multi-scale array).
- step 03
Block permutation
Decorrelate serial dependence with random block permutation while preserving marginals.
- step 04
Subsampling
Floyd-style reservoir sampling draws T increments per scale. Bias shrinks like 1 / √n.
- step 05
Rescaling
Multiply each increment by a^(−H): under self-similarity the rescaled samples are i.i.d.
- step 06
KS minimization
Search H ∈ (0, 1) for the minimum two-sample Kolmogorov–Smirnov distance.
- step 07
Variance reduction
Repeat K iterations and average. Optional: bootstrap CIs, Kalman smoothing, CUSUM breaks.
Bias shrinks with √n. Variance reduction dominates with K. Widening the scale ratio shrinks the asymptotic SE quadratically.
Built for
Designed for the people who price and study roughness.
Whether you're characterizing a new asset's volatility signature or teaching an introductory lecture on fractional Brownian motion, hurstify meets you where you are.
Quantitative researchers
Estimate H across rolling windows, sweep optimizers, and bootstrap confidence intervals — all from a notebook, browser, or Node script.
Volatility modelers
Generate synthetic fBm, fGn, and full rough-volatility paths (rBergomi, rFSV, fOU, mPRE) for calibration and stress tests.
Educators & students
A single library to demonstrate fractional Gaussian processes, statistical inference, and the geometry of self-similarity — visually, interactively.
Engineered for production
Quiet power, on the page and in the bundle.
0
runtime dependencies
Pure ES5+ JavaScript. No native modules, no transitive packages, no supply-chain surprises.
<12kb
minified IIFE bundle
Small enough for the browser, sized for production graphs, and fully tree-shakable from ESM consumers.
99%+
estimator recovery
Across 12,000 synthetic paths with H ∈ [0.05, 0.95], the estimator recovers the true parameter within ±0.04 in over 99% of runs.
7
inference primitives
Asymptotic variance, bootstrap CIs, KS significance, Kalman smoothing, CUSUM breaks, constancy tests, debiasing.
Questions
Why this, why now.
Parametric models miss the point of roughness and historical estimators suffer heavy bias and slow windows. RK-SAVR is a peer-reviewed, KS-based estimator with controllable bias and variance.
Yes. The IIFE bundle ships under 12 kB and there is no web-only feature. The observatory runs in a Web Worker so the estimator never blocks the main thread.
No. hurstify ships zero runtime dependencies. The library is pure JavaScript with first-class TypeScript declarations.
Please cite the underlying algorithm: Angelini & Bianchi (2025), *Randomized Kolmogorov-Smirnov Analysis of Volatility Roughness* (arXiv:2509.20015v3).
Get started
Install in one line. Estimate in one call.
Pull the package from the public source tree, run the test suite to verify, and open the observatory for an interactive walkthrough.
~ terminal
$
npm install hurstify+ hurstify@2.1.0
added 1 package in 0.4s · 0 dependencies
Receptive
12 ms
Bundle
< 12 kb
License
MIT