Marginal Composite Likelihood Estimation of Bergomi Models from High-Frequency Option Prices
Abstract
We develop a theory for estimating the kernel parameters of Bergomi-type stochastic volatility models from option-price time series. The framework allows positive kernels that may be singular at the origin, including the pure power-law kernel of the rough Bergomi model. Using the option-price representation of cumulative forward variance, we formulate the statistical experiment as exact observations of this quantity on increasingly fine time-maturity grids over a fixed horizon. The model has an infinite-dimensional state driven by a single Brownian motion, resulting in a rank-one leading covariance across maturities. Our construction takes maturity differences and then logarithmic time increments. Approximating the resulting diffusion coefficients by maturity-averaged kernels removes the unobserved forward variance curve from the leading term. Positivity of the kernel allows the leading covariance to be recovered from the marginal variances, motivating a weighted marginal composite likelihood contrast. We prove consistency without relative rate restrictions between the time and maturity meshes, allowing the true parameter to lie on the boundary. Under additional regularity and nondegeneracy assumptions and explicit mesh rate conditions, we establish ℱ1-stable asymptotic normality, where ℱ1 is the terminal model σ-field. The Gaussian limit has deterministic sandwich covariance and is independent of ℱ1, so the limit is preserved under equivalent changes of probability measure. We also provide sufficient mesh rate conditions for the pure power-law kernel.
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BibTeX
@misc{tomita2026marginal,
title = {{Marginal Composite Likelihood Estimation of Bergomi Models from High-Frequency Option Prices}},
author = {Haruki Tomita},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40425},
eprint = {2610.40425},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40425},
}
RIS
TY - UNPB
TI - Marginal Composite Likelihood Estimation of Bergomi Models from High-Frequency Option Prices
AU - Haruki Tomita
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40425
UR - https://arxiv.org/abs/2610.40425
AB - We develop a theory for estimating the kernel parameters of Bergomi-type stochastic volatility models from option-price time series. The framework allows positive kernels that may be singular at the origin, including the pure power-law kernel of the rough Bergomi model. Using the option-price representation of cumulative forward variance, we formulate the statistical experiment as exact observations of this quantity on increasingly fine time-maturity grids over a fixed horizon. The model has an infinite-dimensional state driven by a single Brownian motion, resulting in a rank-one leading covariance across maturities. Our construction takes maturity differences and then logarithmic time increments. Approximating the resulting diffusion coefficients by maturity-averaged kernels removes the unobserved forward variance curve from the leading term. Positivity of the kernel allows the leading covariance to be recovered from the marginal variances, motivating a weighted marginal composite likelihood contrast. We prove consistency without relative rate restrictions between the time and maturity meshes, allowing the true parameter to lie on the boundary. Under additional regularity and nondegeneracy assumptions and explicit mesh rate conditions, we establish ℱ_1-stable asymptotic normality, where ℱ_1 is the terminal model σ-field. The Gaussian limit has deterministic sandwich covariance and is independent of ℱ_1, so the limit is preserved under equivalent changes of probability measure. We also provide sufficient mesh rate conditions for the pure power-law kernel.
ER -