Lifting the Heston model

TL;DR

This paper introduces a multi-factor lifted Heston model that bridges classical and rough Heston models, offering improved calibration speed, better short-term implied volatility fits, and efficient simulation while maintaining Markovian properties.

Contribution

The authors propose a multi-factor lifted Heston model that unifies classical and rough Heston models, enhancing calibration and simulation efficiency.

Findings

Model interpolates between classical and rough Heston models.

Achieves fast calibration with few parameters.

Provides efficient simulation schemes.

Abstract

How to reconcile the classical Heston model with its rough counterpart? We introduce a lifted version of the Heston model with n multi-factors, sharing the same Brownian motion but mean reverting at different speeds. Our model nests as extreme cases the classical Heston model (when n = 1), and the rough Heston model (when n goes to infinity). We show that the lifted model enjoys the best of both worlds: Markovianity and satisfactory fits of implied volatility smiles for short maturities with very few parameters. Further, our approach speeds up the calibration time and opens the door to time-efficient simulation schemes.