Efficient option pricing in the rough Heston model using weak simulation schemes

ArXiv ID: 2310.04146 “View on arXiv”

Authors: Unknown

Abstract

We provide an efficient and accurate simulation scheme for the rough Heston model in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$). The scheme is based on low-dimensional Markovian approximations of the rough Heston process derived in [“Bayer and Breneis, arXiv:2309.07023”], and provides weak approximation to the rough Heston process. Numerical experiments show that the new scheme exhibits second order weak convergence, while the computational cost increases linear with respect to the number of time steps. In comparison, existing schemes based on discretization of the underlying stochastic Volterra integrals such as Gatheral’s HQE scheme show a quadratic dependence of the computational cost. Extensive numerical tests for standard and path-dependent European options and Bermudan options show the method’s accuracy and efficiency.

Keywords: Rough Heston model, Markovian approximations, Stochastic Volterra integrals, Bermudan options, Weak approximation, Options / Derivatives

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: The paper features advanced stochastic calculus and functional analysis (fractional kernels, weak convergence analysis), indicating high mathematical complexity. It provides extensive numerical experiments across multiple option types, validating the scheme’s efficiency and accuracy against existing methods.
  flowchart TD
    A["Research Goal:<br/>Develop efficient simulation<br/>for rough Heston model"] --> B["Key Methodology:<br/>Low-dimensional Markovian<br/>approximations<br/>(Bayer & Breneis)"]

    B --> C1["Input Data: <br/>Standard & Hyper-rough regimes"]
    B --> C2["Input Data: <br/>European & Bermudan options"]

    C1 & C2 --> D["Computational Process:<br/>Weak approximation scheme<br/>(2nd order convergence)"]

    D --> E["Key Finding 1:<br/>Linear computational cost<br/>(vs. quadratic for HQE)"]
    D --> F["Key Finding 2:<br/>Accurate pricing for<br/>standard & path-dependent options"]