The notion of market liquidity is nowadays almost ubiquitous. It quantifies the ability of a financial market to match buyers and sellers in an efficient way, without causing a significant movement in the price, thus delivering low transaction costs. It is the lifeblood of financial markets without which market dislocations can show as in the recent well documented crisis: 2007 Yen carry trade unwind, 2008 Credit Crunch, May 6th 2010 Flash Crash or the numerous Mini Flash Crashes occurring in US equity markets, but also in many others cases that go unnoticed but are potent candidates to become more important. While omnipresent, liquidity is an elusive concept. Several reasons may account for this ambiguity; some markets, such as the foreign exchange (FX) market with the daily turnover of $5.3 trillion (let’s say), are mistakenly assumed to be extremely liquid, whereas the generated volume is equated with liquidity. Secondly, the structure of modern markets with its high degree of decentralization generates fragmentation and low transparency of transactions which complicates the way to define market liquidity as a whole. Aggregating liquidity from all trading sources can be quite daunting and even with all of the market fragmentation, as new venues with different market structure continue to be launched. Furthermore, the landscape is continuously changing as new players emerge, such as high frequency traders that have taken over the role of liquidity intermediation in many markets, accounting between 50% and 70% (and ever rising) of all trading. Last, but not least, important participants influencing the markets are the central banks with their myriad of market interventions, whereas it is indirectly through monetization of substantial amount of sovereign and mortgage debt with various quantitative easing programs, or in a direct manner as with Swiss National Bank setting the floor on EUR/CHF exchange rate, providing plenty of arguments they have overstepped their role of last resort liquidity providers and at this stage they hamper market liquidity, potentially exposing themselves to massive losses in the near future.
Despite the obvious importance of liquidity there is little agreement on the best way to measure and define market liquidity. Liquidity measures can be classified into different categories. Volume-based measures: liquidity ratio, Martin index, Hui and Heubel ratio, turnover ratio, market adjusted liquidity index, where, over a fixed period of time, the exchanged volume is compared to price changes. This class implies that non-trivial assumptions are made about the relation between volume and price movements. Other classes of measures include price based measures: Marsh and Rock ratio, variance ratio, vector autoregressive models; transaction costs based measures: spread, implied spread, absolute spread or relative spread see; or time based measures: number of transactions or orders per time unit. The aforementioned approaches suffer from many drawbacks. They provide a top-down approach of analysing a complex system, where the impact of the variation of liquidity is analysed rather than providing a bottom-up approach where liquidity lacking times are identified and quantified. These approaches also suffer from a specific choice of physical time, that does not reflect the correct and multi-scale nature of any financial market. Liquidity is defined as an information theoretic measurement that characterises the unlikeliness of price trajectories and argue that this new metric has the ability to detect and predict stress in financial markets and show examples within the FX market, so that the optimal choice of scales is derived using the Maximum Entropy Principle.