2025/10/09 by Nicola F. Zaugg, Zaugg, Nicola F., Lech A. Grzelak +1 · 1 voice · 1 citation
Economics, Econometrics and Finance · Mathematics · #60-04 #Complex Systems and Time Series Analysis #FOS: Economics and business #Markov Chains and Monte Carlo Methods #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications #q-fin.MF
paper · pdf · doi:10.48550/arxiv.2510.08805
openalex publication_date 2025/10/09 · arxiv published 2025/10/09 · arxiv updated 2025/10/09 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
The lifted Heston model is a stochastic volatility model emerging as a Markovian lift of the rough Heston model and the class of rough volatility processes. The model encodes the path dependency of volatility on a set of N square-root state processes 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 state processes 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 L2 space, the method is optimal in an L2 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.