abaquant.derivatives.calibration.heston

Import path: abaquant.derivatives.calibration.heston

Domain: Derivative pricing, simulation, calibration, diagnostics, and strategy analysis.

Purpose

Heston implied-volatility calibration.

When to use it

This module fits model parameters to observations. Inspect convergence status, residual scale, bounds, weighting, and data provenance before treating fitted parameters as stable estimates.

Public objects

  • function: calibrate_heston — Calibrate Heston parameters to a cross-section of market implied volatilities.

Detailed reference

Heston implied-volatility calibration.

Purpose

The module fits Heston model parameters to a supplied cross-section of market implied volatilities by constrained numerical minimisation.

Conventions

Strikes and spot share units; maturity is in years; rates and dividends are decimal annual rates; implied volatilities are decimal annual quantities.

References

[ 1 ] Heston, S. L. (1993), “A Closed-Form Solution for Options with Stochastic Volatility”.

abaquant.derivatives.calibration.heston.calibrate_heston(S, T, r, q, strikes, market_ivs, kappa0=2.0, theta0=0.04, xi0=0.3, rho0=-0.5, v00=0.04, method='L-BFGS-B', tol=1e-8, max_iter=300)

Calibrate Heston parameters to a cross-section of market implied volatilities.

Parameters:

  • S (float or array-like) – Current underlying spot price in currency units.

  • T (float or array-like) – Time to maturity in years.

  • r (float or array-like) – Continuously compounded risk-free annual rate in decimal units.

  • q (float or array-like) – Continuous dividend or carry yield in decimal annual units.

  • strikes (float or array-like) – Strike-price grid in the same currency units as the underlying or forward.

  • market_ivs (float or array-like) – Observed market implied volatilities, expressed as annualized decimals.

  • kappa0 (float, default=2.0) – Initial calibration guess for Heston kappa.

  • theta0 (float, default=0.04) – Initial calibration guess for Heston theta.

  • xi0 (float, default=0.3) – Initial calibration guess for Heston xi.

  • rho0 (float, default=-0.5) – Initial calibration guess for Heston rho.

  • v00 (float, default=0.04) – Initial calibration guess for Heston initial variance.

  • method (str, default='L-BFGS-B') – Optimization method name accepted by the underlying solver.

  • tol (float, default=1e-08) – Numerical convergence tolerance.

  • max_iter (int, default=300) – Maximum numerical-optimizer or root-finder iterations.

Returns:

Computed calibrate heston in the units implied by the documented inputs.

Return type:

float

Notes

Model inputs are interpreted according to the module-level rate, maturity, and volatility conventions. Numerical outputs depend on the validity of those assumptions.