Year: 2026
Type: article
Abstract: This is the second part of our work on Multivariate Quadratic Hawkes (MQHawkes) processes, devoted to the calibration of the model defined and studied analytically in Aubrun, C., Benzaquen, M., & Bouchaud, J. P., Quantitative Finance, 23(5), 741–758 (2023). We propose a non-parametric calibration method based on the method of moments applied to a coarse-grained version of the MQHawkes model. This allows us to bypass challenges inherent to tick-by-tick data. Our main methodological innovation is a multi-step calibration procedure, first focusing on ‘self’ feedback kernels, and then progressively including cross-effects. Indeed, while cross-effects are significant and interpretable, they are usually 1 order of magnitude smaller than self-effects and must therefore be disentangled from noise with care. For numerical stability, we also restrict to pair interactions and only calibrate bi-variate QHawkes, neglecting higher-order interactions. Our main findings are as follows: (a) While cross-Hawkes feedback effects have been empirically studied previously, cross-Zumbach effects are clearly identified here for the first time. The effect of recent trends of the e-mini futures contract onto the volatility of other futures contracts is especially strong. (b) We have identified a new type of feedback that couples past realized covariance between two assets' returns and future volatility of these two assets, with the pair e-mini–tbond as a case in point. (c) A cross-leverage effect, whereby the sign of the return of one asset impacts the volatility of another asset, is also clearly identified. The cross-leverage effect between the e-mini and the residual volatility of single stocks is notable, and surprisingly universal across the universe of stocks that we considered.
Source: Quantitative Finance
Language: English
Subfield: Finance
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4414790747
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