13-APR-2026
We develop a Wishart stochastic volatility framework for the two-sided futures order book and establish its role as the correct continuum limit of the multivariate FTQR-Hawkes microstructure model. The variance state $V(t)$ evolves as a $2 \times 2$ positive-definite matrix CIR process, capturing the full covariation $v_{12}(t)$ between bid-side and ask-side volatility — a quantity that the Double Heston model is structurally forced to set to zero. We prove that the Wishart model retains an exponential-affine characteristic function, with the matrix Riccati ODE solved via a $4 \times 4$ Hamiltonian matrix exponential, enabling Carr-Madan FFT calibration to the joint call-put option surface. The off-diagonal entry $v_{12}(0)$ recovered from this calibration initialises the Hawkes cross-excitation matrix $\alpha_{12}$, and three mean-field game systems yield rational intensity benchmarks $\lambda^*_b$, $\lambda^*_a$ whose signed divergence from empirical intensities generates high-conviction intraday trading signals.
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