We introduce a structure of an infinite-dimensional Frobenius manifold on a subspace in the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/∞, respectively. The dispersionless 2D Toda equations are embedded into a bigger integrable hierarchy associated with this Frobenius manifold.

Abstract. We define a dispersionless tau-symmetric bihamiltonian integrable hierarchy on the space of pairs of functions analytic inside/outside the unit circle with simple poles at 0/∞ respectively, which extends the dispersionless 2D Toda hierarchy of Takasaki and Takebe. Then we construct the deformed flat connection of the infinite-dimensional Frobenius manifold M 0 introduced by Carlet, Dubrovin and Mertens in Math. Ann. 349 (2011) 75-115 and, by explicitly solving the deformed flatness equations, we prove that the extended 2D Toda hierarchy coincides with principal hierarchy of M 0 .

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Market liquidity is a latent and dynamic variable. We propose a dynamical linear price impact model at high-frequency in which the price impact coefficient is a product of a daily, a diurnal, and an autoregressive stochastic intraday component. We estimate the model using a Kalman filter on order book data for stocks traded on the NASDAQ in 2016. We show that our price changes estimates conditional on order flow imbalance explain, on average, 82% of real price changes variance. Evidence is also provided on the fact that the conditioning on filtered information improves the estimate of the LOB liquidity with respect to the one obtained from a static estimation of the price impact. In addition, an out-of-sample analysis shows that our model provides a superior out-of-sample forecast of price impact with respect to historical estimates.

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