Buy and prices go up, sell and prices go down. Going beyond this (too) simple picture uncovers a very complex price impact mechanism and a sometimes counter-intuitive behaviour of financial markets.
Salient empirical observations include highly non-linear and non-Markovian market impacts on stock/future markets and the Bitcoin exchanges. We present an overview of empirical facts and recent developments in market impact theory with a focus on statistical order book models. We introduce a non-linear, minimal, consistent model which generalizes previous linear models of impact. Applications to optimal execution strategies for large orders, stock-pinning for Delta-hedged options and dynamical arbitrage are discussed.
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