Documentation

Overview

Volptima provides CVI (Convex Volatility Interpolation), a volatility surface fitter built on convex optimization. Instead of starting from a parametric model, CVI formulates the calibration as a sparse quadratic program, enforcing no-butterfly and no-calendar arbitrage as hard constraints, and more generally encoding the structural properties of the volatility surface. You send market data (bid/ask quotes in vol or price space) and get back a fitted surface you can interpolate at any strike. Those two spaces are the two APIs: the Vol API (you supply implied volatilities) or the Price API (you supply raw option prices), both returning the same fitted CVI surface, so only the input differs.

You reach either API through one of two interfaces: the Python API Client (which fits locally via grafit or in the cloud) or grafit directly (Rust, with Python and C bindings) for non-Python or low-level use.

Beyond CVI, the library also provides a fast American option pricer (supporting discrete cash dividends) with smooth greeks.

Plug and Play

Volptima works out of the box. There is no model to choose, and no need to tune hyperparameters: the defaults are sensible and work across assets. From market quotes to volatility surfaces. It just works.

Two APIs

Both APIs drive the same core CVI fitter; they differ only in what you feed it. The Vol API takes implied volatilities and feeds CVI directly. The Price API adds a layer on top of CVI: it takes raw option prices and backs the vols out for you (and the forward and discount factor too, when omitted) before fitting.

The Vol API is European only and needs the forward and discount factor up front. The Price API also handles American exercise, calibrates the forward and discount factor from the quotes when you omit them (though an American expiry must still pin its discount factor), and accepts cash dividends for American expiries.

Market Data

Volptima does not provide market data. Typically you pass a snapshot of all the listed option quotes of a given underlying through the Price API, along with expectations of future cash dividends for American options.

What You Get

Whichever API you use, the fitter takes market data and returns a fitted volatility surface with these parameters per expiry:

The fitted surface is arbitrage-free by construction: no butterfly arbitrage (PDF ≥ 0) and no calendar arbitrage (total variance non-decreasing).

Two Interfaces

Architecture

How a request flows from your code to the fitter:

SaaS clients use the API Client with CloudBackend (cloud fitting, no local install). Grafit clients can use the API Client with LocalBackend, or call Grafit directly from any supported language.

Typical Workflow: Shared Discount Factor

A discount factor is the same for every underlying denominated in a given currency, yet it is hard to back out from a single name's American quotes. A common pattern: first fit the most liquid European product in the currency (for example SPX for USD) with the Price API and let it calibrate the forward and discount factor from the quotes. Then reuse that discount factor for the other underlyings in the same currency: pin it on each fit (required for American expiries) and supply cash dividends for American names, so every surface shares one consistent, market-implied discount factor.

Advanced Workflow: Multi-Snapshot Forward & Discount-Factor Stabilization

Fitting one snapshot at a time can leave the forward and discount factor noisy, especially before events when market makers widen their quotes. The forward/spot basis, though, is far more stable than the forward itself (the forward moves with the spot), so the basis can be stabilized across multiple snapshots and recombined with the live spot for a clean forward. The discount factor, generally stable too, is handled the same way. This sits on top of the single-snapshot Price API.