Marginal Composite Likelihood Estimation of Bergomi Models from High-Frequency Option Prices

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 $\mathscr F_1$-stable asymptotic normality, where $\mathscr F_1$ is the terminal model $σ$-field. The Gaussian limit has deterministic sandwich covariance and is independent of $\mathscr F_1$, so the limit is preserved under equivalent changes of probability measure. We also provide sufficient mesh rate conditions for the pure power-law kernel.