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Simulation of square-root processes made simple: applications to the Heston model

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arxiv 2412.11264 v2 pith:3EQTPQBP submitted 2024-12-15 q-fin.MF q-fin.CP

Eduardo Abi Jaber This is my paper · ORCID
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keywords processsquare-rootintegratedhestonhighmodelnumericalscheme
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We introduce a simple, efficient and accurate nonnegative preserving numerical scheme for simulating the square-root process. The novel idea is to simulate the integrated square-root process first instead of the square-root process itself. Numerical experiments on realistic parameter sets, applied for the integrated process and the Heston model, display high precision with a very low number of time steps. As a bonus, our scheme yields the exact limiting Inverse Gaussian distributions of the integrated square-root process with only one single time-step in two scenarios: (i) for high mean-reversion and volatility-of-volatility regimes, regardless of maturity; and (ii) for long maturities, independent of the other parameters.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Diffusion bridge with randomized initial and terminal times and its application to fish migration

    q-bio.PE 2026-07 conditional novelty 6.5 of 10

    A well-posed CIR bridge with time-changed random initial and terminal times models water-temperature-driven Ayu migration and is explored on fish-count and eDNA data.

  2. Stochastic partial differential equation model for environmental DNA dynamics in river environments

    q-bio.QM 2026-08 conditional novelty 6.0 of 10

    An affine SPDE with delayed source connects fish migration counts to riverine eDNA concentration, with closed-form Laplace functional and nonnegativity-preserving numerics.

  3. CIR bridge for modeling of fish migration on sub-hourly scale

    math.PR 2025-06 conditional novelty 6.0 of 10

    A CIR bridge with closed-form mean and variance is proposed and fitted to sub-hourly ayu migration counts, capturing the observed bursty intermittency.

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