qsmile¶

Volatility smile fitting for quantitative finance

qsmile is a Python library for fitting parametric volatility smile models to option chain data. It provides bid/ask-aware data containers, Black76 pricing, forward/discount-factor calibration, and least-squares SVI calibration out of the box.

Features¶

• Bid/ask option prices — OptionChain stores bid/ask call and put prices, and automatically calibrates the forward and discount factor from put-call parity using quasi-delta weighted least squares.
• Coordinate transforms — VolData is a unified container with .transform(x, y) to freely convert between any combination of X-coordinates (Strike, Moneyness, Log-Moneyness, Standardised) and Y-coordinates (Price, Volatility, Variance, Total Variance) via composable, invertible maps.
• SVI fitting — Fit the SVI raw parameterisation to VolData:

where \(k = \ln(K/F)\) is log-moneyness and \(w\) is total implied variance.

• SABR model — Fit the SABR stochastic volatility model.
• Black76 pricing — Vectorised call/put pricing and explicit closed-form implied vol inversion via black76_call, black76_put, and black76_implied_vol. The inverter uses the inverse-Gaussian quantile representation of Schadner (2026), which recovers implied vol to machine precision in a single non-iterative evaluation.
• Plotting — All chain types have a .plot() method for bid/ask error-bar charts (requires qsmile[plot]).

Quick Example¶

import numpy as np
import pandas as pd
from qsmile import SmileMetadata, SVIModel, VolData, fit

meta = SmileMetadata(
    date=pd.Timestamp("2024-01-01"),
    expiry=pd.Timestamp("2024-07-01"),
    forward=100.0,
)

sd = VolData.from_mid_vols(
    strikes=np.array([80, 90, 100, 110, 120], dtype=float),
    ivs=np.array([0.28, 0.22, 0.18, 0.17, 0.19]),
    metadata=meta,
)

result = fit(sd, model=SVIModel)
print(result.model)    # Fitted SVIModel
print(result.rmse)     # Root mean square error

Getting Started¶

Install with pip:

pip install qsmile            # core
pip install "qsmile[plot]"    # with matplotlib plotting

Explore the API Reference for full documentation, or try the interactive Marimo Notebooks.