Paper: arXiv 2510.08805

Authors: Nicola F. Zaugg, Lech A. Grzelak

Abstract

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework for simulating the Lifted Heston model using an L2 linear projection and Inverse Gaussian sampling. While heavy on stochastic calculus and theoretical derivations, it provides concrete Monte Carlo application methods and makes Python code publicly available on GitHub.

Research Flowchart

  flowchart TD
    A["Research Goal: Efficient Monte Carlo Simulation<br/>for Lifted Heston Model with Large Steps"] --> B["Input Data: Model Parameters &<br/>Common Stochastic Factor"]
    B --> C["Establish L2 Optimal Linear Projection<br/>between Stochastic Driver & Integrated Variance"]
    C --> D["Sample Conditional Integrated Variance<br/>using Inverse Gaussian Distribution"]
    D --> E["Implicit Integrated Variance<br/>Simulation Scheme"]
    E --> F["Outcomes: Near-Exact Accuracy with Large Time Steps<br/>& Efficient Pricing of Volatility Options"]

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2 of 28 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.