Lifting the Heston model

Eduardo Abi Jaber (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Mots clés: rough volatility; affine Volterra processes; implied volatility; Stochastic volatility; Riccati equa- tions; Riccati equa-tions

Domaines: Finance quantitative [q-fin.CP]; Probabilités [math.PR]

Eduardo Abi Jaber. Lifting the Heston model. Quantitative Finance, In press. ⟨hal-01890751v2⟩