Abstract:We propose a quasi maximum likelihood estimation method for Bergomi-type stochastic volatility models with parametrized kernels, focusing on the estimation of the kernel parameters from high-frequency time-series observations of option prices. We first show that the cumulative forward variance, which can be reconstructed from option prices, solves an infinite-dimensional stochastic differential equation driven by a one-dimensional Brownian motion under the Bergomi-type model. To overcome this degeneracy, we introduce a nondegenerate proxy likelihood based on the Euler-Maruyama approximation and define an estimator through the associated estimating function. We establish consistency and asymptotic mixed normality of the proposed estimator under a regular class of kernels. Simulation studies and an empirical application to SPXW option data illustrate the finite-sample performance of the method and the practical relevance of the approach.
| Comments: | 27 pages, 3 figures |
| Subjects: | Statistics Theory (math.ST) |
| Cite as: | arXiv:2605.25359 [math.ST] |
| (or arXiv:2605.25359v1 [math.ST] for this version) | |
| https://doi.org/10.48550/arXiv.2605.25359 arXiv-issued DOI via DataCite (pending registration) |
From: Haruki Tomita [view email]
[v1]
Mon, 25 May 2026 02:28:35 UTC (784 KB)
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