Lifted Heston Model: Efficient Monte Carlo Simulation with Large Time Steps

Abstract. The lifted Heston model [E. Abi Jaber, Quantitative Finance, 19 (2019), pp. 1995–2013] is a stochastic volatility model emerging as a Markovian lift of the rough Heston model [O. El Euch and M. Rosenbaum, Mathematical Finance, 29 (2019), pp. 3–38] and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of [Formula: see text] square-root latent factors driven by a common stochastic factor. While the system is Markovian, simulation schemes such as the Euler scheme exist but require a small-step, multidimensional simulation of the latent factors and are therefore numerically challenging. We propose a novel simulation scheme of the class of implicit integrated variance schemes. The method exploits the near-linear nature between the stochastic driver and the conditional integrated variance process, which allows for a consistent and efficient sampling of the integrated variance process using an inverse Gaussian distribution. Since we establish the linear relation using a linear projection in the [Formula: see text] space, the method is optimal in an [Formula: see text] sense and offers a significant efficiency gain over similar methods. We demonstrate that our scheme achieves near-exact accuracy even for coarse discretizations and allows for efficient pricing of volatility options with large time steps.