Correlation emergence and the Epps effect in two coupled limit order books (opens in new tab)

We give a unified analytic account of correlation emergence and the Epps effect in two coupled limit order books. The model starts from a discrete random-walk description of order flow with creation, cancellation and diffusion. A pair-trader coupling between the books is introduced at the level of order creation. We clarify how the discrete model reduces to coupled reaction--diffusion equations with a moving reaction boundary defining the transa...