Mathematical Modelling of Liquidity Risk in Financial Markets

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In financial markets, an asset such as a stock, a bond or a commodity is said to be illiquid when large quantities cannot always be traded at any desired time (buyers and sellers are not always available), when the added cost of trading large quantities, or liquidity premium, is non-negligible, or when the impact of a large transaction on prices persists over time. Liquidity becomes a risk factor when its level evolves randomly in time. In recent years, the availability of limit order book data has made liquidity risk the focal point of many trading desks around the world. From a mathematical modelling point of view, only the last two dimensions of illiquidity have been considered in details in the academic literature. Furthermore, these two notions have usually been