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We propose a series of simple models for the microstructure of a double auction market without intermediaries. We specialize to those markets, such interdealer broker markets, which are dominated by professional traders, who trade mainly through limit orders, watch markets closely, and move their limit order prices frequently. We model these markets as a set of buyers and a set of sellers diffusing in price space and…
We have discovered 12 independent new empirical scaling laws in foreign exchange data-series that hold for close to three orders of magnitude and across 13 currency exchange rates. Our statistical analysis crucially depends on an event-based approach that measures the relationship between different types of events. The scaling laws give an accurate estimation of the length of the price-curve coastline, which turns ou…
Intrinsic time is an example of an event-based conception of time, used to analyze financial time series. Here, for the first time, we reveal the connection between intrinsic time and physical time. In detail, we present an analytic relationship which links the two different time paradigms. Central to this discovery are the emergence of scaling laws. Indeed, a novel empirical scaling law is presented, relating to the…
We introduce a novel framework for developing fully-automated trading model algorithms. Unlike the traditional approach, which is grounded in analytical complexity favored by most quantitative analysts, we propose a paradigm shift that embraces real-world complexity. This approach leverages key concepts relating to self-organization, emergence, complex systems theory, scaling laws, and utilizes an event-based reframi…
This paper examines the short-term asymptotic behavior of the implied volatility surface, focusing on the at-the-money (ATM) skew and curvature. Rather than committing to a specific stochastic differential equation, we adopt a distribution-based approach by imposing cumulant conditions on the log-return distribution. Under these weak assumptions, we derive a quadratic expansion of implied volatility as a function of …
Understanding the structure of financial markets deals with suitably determining the functional relation between financial variables. In this respect, important variables are the trading activity, defined here as the number of trades $N$, the traded volume $V$, the asset price $P$, the squared volatility $σ^2$, the bid-ask spread $S$ and the cost of trading $C$. Different reasonings result in simple proportionality r…
We confirm and substantially extend the recent empirical result of Andersen et al. \cite{Andersen2015}, where it is shown that the amount of risk $W$ exchanged in the E-mini S\&P futures market (i.e. price times volume times volatility) scales like the 3/2 power of the number of trades $N$. We show that this 3/2-law holds very precisely across 12 futures contracts and 300 single US stocks, and across a wide range of …
The trade size $ω$ has direct impact on the price formation of the stock traded. Econophysical analyses of transaction data for the US and Australian stock markets have uncovered market-specific scaling laws, where a master curve of price impact can be obtained in each market when stock capitalization $C$ is included as an argument in the scaling relation. However, the rationale of introducing stock capitalization in…
For a sequence of binary bets, the Kelly criterion provides a closed-form solution that maximizes the expected growth rate of wealth. In contrast, when multiple bets are placed simultaneously (e.g., in portfolio allocation or prediction markets), the optimal Kelly strategy generally requires numerical optimization over a joint outcome space. A naive formulation scales exponentially in the number of bets, requiring $O…
Is there a general economic pathway recapitulated by individual cities over and over? Identifying such evolution structure, if any, would inform models for the assessment, maintenance, and forecasting of urban sustainability and economic success as a quantitative baseline. This premise seems to contradict the existing body of empirical evidences for path-dependent growth shaping the unique history of individual citie…
This short note is intended as a "Letter to the Editor" Perspective in order that it serves as a contribution, in view of reaching the physics community caring about rare events and scaling laws and unexpected findings, on a domain of wide interest: sport and money. It is apparent from the data reported and discussed below that the scarcity of such data does not allow to recommend a complex elaboration of an agent ba…
Liquidity providers (LPs) on decentralized exchanges (DEXs) can protect themselves from adverse selection risk by updating their positions more frequently. However, repositioning is costly, because LPs have to pay gas fees for each update. We analyze the causal relation between repositioning and liquidity concentration around the market price, using the entry of blockchain scaling solutions, Arbitrum and Polygon, as …
Loss-versus-Rebalancing (LVR) is the dominant adverse-selection cost borne by liquidity providers on automated market makers. Under geometric Brownian motion, arbitrage profit scales with the probability of a profitable block, which vanishes as the block time $Δt \to 0$; this is the standing argument for ever-shorter blocks. Modeling the reference price instead as a jump-diffusion, I show that the constant-product LV…
Public blockchains can make many trading venues simultaneously visible and mechanically reachable, yet an order still has to pay to activate each additional venue: technological connectivity need not translate into economically integrated execution. Automated-market-maker (AMM) pools make this gap directly measurable, because exact pre-trade venue states, transaction-level routing costs, and realized venue use can be…
We show that net demand for liquidity by algo strategies is identifiable from its trade and price history alone, with no knowledge of its signal or optimization problem. An exact multi-period regret decomposition implies that the sign of this statistic classifies a linear strategy as a net liquidity consumer or provider, recovering the Kyle (1985) informed-trader/market-maker dichotomy from observables alone. Under a…
We propose a microstructural model for the order flow in financial markets that distinguishes between {\it core orders} and {\it reaction flow}, both modeled as Hawkes processes. This model has a natural scaling limit that reconciles a number of salient empirical properties: persistent signed order flow, rough trading volume and volatility, and power-law market impact. In our framework, all these quantities are pinne…
We establish a general matched filter principle for order flow normalization: optimal normalization must match the scaling behaviour of the signal-generating process. For capacity-constrained institutional investors, market capitalization normalization ($S^{MC}$) is the matched filter; for volume-targeting traders (e.g., VWAP/TWAP algorithms), trading value normalization ($S^{TV}$) is optimal. Monte Carlo simulations…
We present a reproducible research framework for market microstructure combining a deterministic C++ limit order book (LOB) simulator with stochastic order flow generated by multivariate marked Hawkes processes. The paper derives full stability and ergodicity proofs for both linear and nonlinear Hawkes models, implements time-rescaling and goodness-of-fit diagnostics, and calibrates exponential and power-law kernels …