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arxiv: 2604.27210 · v1 · submitted 2026-04-29 · 💱 q-fin.CP · cs.MS· q-fin.MF· q-fin.PR

Recognition: unknown

Fast-Vollib: A Fast Implied Volatility Library for Pythonwith PyTorch, JAX, and CUDA Fused-Kernel Backends

Raeid Saqur

Pith reviewed 2026-05-07 10:39 UTC · model grok-4.3

classification 💱 q-fin.CP cs.MSq-fin.MFq-fin.PR
keywords implied volatilityEuropean optionsBlack-ScholesPython libraryPyTorchJAXCUDATriton
0
0 comments X

The pith

Fast-vollib provides high-performance European option pricing, implied volatility, and Greeks as a drop-in replacement for py_vollib using PyTorch, JAX, and CUDA backends.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents fast-vollib, an open-source Python library for high-performance European option pricing, implied volatility computation, and Greeks under the Black-76, Black-Scholes, and Black-Scholes-Merton models. It supplies pluggable execution backends for PyTorch, JAX, and CUDA via Triton fused kernels, plus a vectorized Halley-method solver and an experimental fully-vectorized implementation of Jäckel's Let's Be Rational algorithm for batched option chains. The library maintains a compatibility-first public API so that existing code can adopt it without modification. A sympathetic reader would care because repeated implied-volatility calculations on large option datasets appear in pricing, hedging, and risk systems, where faster execution reduces latency in those workflows.

Core claim

Fast-vollib is an open-source library that implements European option pricing, implied volatility computation, and Greeks under Black-76, Black-Scholes, and Black-Scholes-Merton models. It supplies pluggable PyTorch, JAX, and CUDA-Triton backends, a vectorized Halley-method IV solver, and an experimental fully-vectorized Jäckel Let's Be Rational algorithm with NumPy/Numba, torch.compile, JAX, and single-pass GPU kernels for batched workloads.

What carries the argument

Pluggable execution backends (PyTorch, JAX, Triton) paired with vectorized implied-volatility solvers that support batched processing across hardware and automatic-differentiation frameworks.

Load-bearing premise

The claimed performance gains, numerical correctness, and API compatibility hold across the supported backends and workloads.

What would settle it

A direct benchmark run on representative option chains that shows either slower wall-clock times than py_vollib or implied-volatility outputs differing by more than machine precision.

Figures

Figures reproduced from arXiv: 2604.27210 by Raeid Saqur.

Figure 1
Figure 1. Figure 1: The four rational-initial-guess regimes of the normalised Black function used by the LBR algorithm. Each regime uses a separate rational approximation before Householder(3) refinement. 2.2 API Surface view at source ↗
read the original abstract

We present fast-vollib, an open-source Python library that provides high-performance European option pricing, implied volatility (IV) computation, and Greeks under the Black-76, Black-Scholes, and Black-Scholes-Merton models. The library is designed as a drop-in alternative to the de-facto-standard py_vollib and py_vollib_vectorized packages, with pluggable PyTorch and JAX execution backends, a CUDA fused-kernel Triton contribution for batched IV workloads, and a compatibility-first public API. In addition to a vectorized Halley-method IV solver, fast-vollib ships an experimental, fully-vectorized implementation of J\"ackel's "Let's Be Rational" (LBR) algorithm with NumPy/Numba, torch.compile, JAX, and Triton single-pass GPU kernels for batched option chains. This note announces the library and describes its public API surface, with source, documentation, and packaging artifacts available at: GitHub (https://github.com/raeidsaqur/fast-vollib), Docs (https://raeidsaqur.github.io/fast-vollib/), PyPI (https://pypi.org/project/fast-vollib/).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript announces fast-vollib, an open-source Python library for high-performance European option pricing, implied volatility computation, and Greeks under the Black-76, Black-Scholes, and Black-Scholes-Merton models. It features pluggable PyTorch, JAX, and CUDA fused-kernel Triton backends, a vectorized Halley-method IV solver, and an experimental fully-vectorized implementation of Jäckel's Let's Be Rational algorithm, positioning itself as a drop-in replacement for py_vollib with source, documentation, and PyPI artifacts available externally.

Significance. If the performance and compatibility claims are substantiated, the library would provide a useful high-performance tool for quantitative finance practitioners, especially those integrating option pricing with PyTorch or JAX workflows. The multi-backend architecture and experimental vectorized LBR implementation are positive contributions to reproducible computational finance software. The open-source release and compatibility focus are explicit strengths.

major comments (1)
  1. Abstract and manuscript body: the central claims of 'high-performance', 'fast' execution, and 'drop-in' compatibility with py_vollib are presented without any benchmark timings, accuracy comparisons to existing libraries, error analysis, or validation results. These empirical elements are load-bearing for evaluating the library's contribution, as the text relies entirely on external repository links rather than contained evidence.
minor comments (1)
  1. The manuscript is concise and refers readers to GitHub/Docs/PyPI for all implementation details; incorporating a short self-contained usage example or API snippet would improve readability and independence from external resources.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of the library's potential utility and for the constructive critique regarding empirical substantiation. We address the single major comment below and commit to a revision that incorporates the requested evidence directly into the manuscript.

read point-by-point responses

  1. Referee: Abstract and manuscript body: the central claims of 'high-performance', 'fast' execution, and 'drop-in' compatibility with py_vollib are presented without any benchmark timings, accuracy comparisons to existing libraries, error analysis, or validation results. These empirical elements are load-bearing for evaluating the library's contribution, as the text relies entirely on external repository links rather than contained evidence.

    Authors: We agree that the current short announcement format leaves the performance and compatibility claims without self-contained empirical support, which weakens the manuscript's ability to stand alone. In the revised version we will add a dedicated 'Performance and Validation' section containing: (i) wall-clock timing tables for batched pricing and IV computation across NumPy, PyTorch, JAX, and Triton backends for representative batch sizes (1k–1M options); (ii) direct accuracy and runtime comparisons against py_vollib and py_vollib_vectorized on identical test vectors; (iii) convergence and error statistics for the vectorized Halley and experimental LBR solvers (maximum absolute error, iteration counts, and failure rates versus reference implementations); and (iv) a brief validation subsection confirming Greeks and model prices against closed-form expectations and known test suites. Representative figures and tables will be generated from the existing benchmarking scripts already present in the repository. This revision will make the claims verifiable without requiring the reader to consult external links. revision: yes

Circularity Check

0 steps flagged

No significant circularity; software library announcement

full rationale

The manuscript is a concise library announcement describing an open-source Python package for European option pricing, IV computation, and Greeks under standard Black-76/BS/BSM models. It implements known algorithms (vectorized Halley solver, experimental Jäckel LBR) via pluggable backends but contains no derivations, equations, fitted parameters, or predictions. All substantive claims are supported by external links to GitHub, documentation, and PyPI rather than internal reductions or self-citations. No load-bearing steps reduce to inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This preprint announces a software library implementing known numerical methods rather than presenting a mathematical derivation or empirical study. No free parameters are fitted, no axioms are postulated, and no new entities are invented.

pith-pipeline@v0.9.0 · 5525 in / 1323 out tokens · 66847 ms · 2026-05-07T10:39:57.600830+00:00 · methodology

discussion (0)

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Reference graph

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