VIXRHeston

VIXRHeston is a lightweight Python package for computing the VIX term structure in the rough Heston model via a Markovian (lifted Heston) approximation. Using the paper’s key result that, under the lifted model, squared VIX (VIX²) admits an analytical expression (linear in the Markovian variance components), the package evaluates

VIX^2(t, τ) = (1/τ) * integral from t to t+τ of E_t[V_s] ds

efficiently across maturities, avoiding nested Monte Carlo simulation. This enables fast generation of the full VIX term structure and supports calibration workflows requiring repeated VIX evaluations.

Installation

From PyPI

pip install VIXRHeston

Quick start

import numpy as np
from VIXRHeston import vec_c, vec_x
from VIXRHeston import squared_VIX

H,n = 0.1,2
alpha, rn= H+0.5, 1+10*(1/(n)**0.9)
c, x = vec_c(n,rn,alpha), vec_x(n,rn,alpha)
t, tau = 0, 1/12
rho, lamb,theta,nu,V0 = -0.7,0.1,0.03,0.3, 0.01
VIX2 = squared_VIX(t, c, x, V0,lamb,theta,nu,rho, tau)
VIX  = np.sqrt(VIX2)
print(VIX)

License

MIT License. See LICENSE.

References

Ye, Y., Fan, Z., & Kwok, Y. K. (2026). VIX term structure in the rough Heston model via Markovian approximation. Journal of Futures Markets, forthcoming.