Correlation emergence and the Epps effect in two coupled limit order books

Battle Count: 86

The paper provides fundamental understanding of how cross-asset correlations emerge and decay at different timescales (Epps effect), which is directly relevant to pairs trading, statistical arbitrage, and multi-asset strategy design. However, it is primarily a theoretical/analytical contribution rather than a practical trading system. The separation of clock and coupling mechanisms helps practitioners understand whether observed correlation decay is due to sampling artifacts or genuine slow coupling response.

The model involves fractional reaction-diffusion PDEs, discrete random walks with memory kernels (Sibuya), moving boundary problems, inverse stable subordinators, Mittag-Leffler functions, and regularised coupling sources. The numerical implementation requires careful handling of operational-time evolution, reaction-front tracking, translation-mode coupling, and separate calendar-time observation clocks. The analytical derivations span multiple appendices with detailed validity conditions.

Code and numerical outputs are available from the University of Cape Town reproducibility archive (doi:10.25375/uct.33368986.v1) and a public GitHub repository. The paper provides detailed appendices with all derivations, assumptions, and validity conditions. No empirical market data are used; all results are from simulation and analytical derivation.