noscript .site-navigation .nav-menu-toggle { display: none; } @media (max-width: 1023px) { noscript .site-navigation { position: relative; background: var(--ink); } noscript .site-navigation .nav-mobile-menu { position: relative; inset: auto; margin: 0 16px 16px; display: block; visibility: visible; opacity: 1; pointer-events: auto; transform: none; transition: none; } noscript .site-navigation .nav-mobile-menu-inner { max-height: none; overflow: visible; } noscript .site-navigation .nav-mobile-links li, noscript .site-navigation .nav-mobile-contact-wrap { opacity: 1; transform: none; transition: none; } } 市場信號鎖定深度矢量執行軌道循環驗證噪聲過濾解析掃描隱藏流動結構映射就緒時鐘穩定延遲價差權重更新歸一化失衡核微觀結構追蹤萊利研究核心同步執行算法

DESIGNING THE FUTURESTAKES OFALGORITHMS

Financial markets can be as chaotic and unpredictable as the weather. Beneath that complexity lie patterns that finer-grained data and AI can help reveal. Rayleigh Research develops technologies to simulate market behaviour, explore intelligent algorithms, and design market mechanisms for order-book markets more broadly, with an initial focus on digital assets. The future is decentralised.

The Rayleigh Criterion

Resolving Markets at the Limits of Precision

High-frequency markets evolve through interactions that conventional market data may not fully capture. Inspired by the Rayleigh Criterion, we focus on resolving fine-grained order-book dynamics with Deep High-Frequency Data (DHFD) to support more realistic market simulations, algorithm evaluation, and risk analysis.

Exploring signal resolution

Explore two illustrative signals. Move the slider to see how their overlap changes as their separation increases.

Broader combined curve Narrower combined curve Illustrative signals A and B

Explore signal separation

Closer togetherFarther apart

Signal positions change in this illustration. Curve heights are normalised for comparison. This is not a measured financial-resolution threshold.

Deep High-Frequency Data (DHFD)Fine-grained market data underlying its reconstruction and simulation work. The curves above illustrate the idea of distinguishing nearby signals; they do not display DHFD or actual market events.

What the visual shows

The two peaks are illustrative signals, not actual market orders. Moving them farther apart makes their contributions easier to distinguish. This introduces the idea of resolution: whether nearby events can be seen separately. In financial markets, the related question is how much detail an observation preserves.

Why this matters

A market-price summary does not show every order being added, changed or cancelled. Fine-grained limit-order-book data can preserve more of that activity for market reconstruction and simulation. This supports more detailed evaluation of trading algorithms and risk, without guaranteeing predictive accuracy or profitable trading.

θ = 1.21967 · λ / D

In optics, θ is the approximate minimum angular separation at which two point sources can be distinguished. λ is the wavelength of light, and D is the diameter of the circular aperture. As a conceptual financial analogy, Rayleigh relates λ to sampling granularity and D to the amount of market data available for representing orders, liquidity changes, and participant interactions.

The Rayleigh Criterion remains an optical formula. Its application here is conceptual, illustrating the importance of data resolution rather than defining a validated financial market equation.

Up next in Our ApproachSimulated RealityCompare market modelling approaches

Simulated Reality

No single simulation method captures every aspect of financial market behaviour. Rayleigh Research develops complementary approaches to modelling and simulation, combining mathematical frameworks, fine-grained historical market data, and decentralised AI-agent environments. Each addresses different needs in algorithm evaluation, risk management, and market-mechanism development.

Blurred

01Blurred

Standard

Conventional historical backtesting evaluates trading algorithms against sampled, historical market data, using past observations to assess strategy behaviour under recorded market conditions. It provides a useful baseline for comparing different trading strategies, but does not represent market impact, fine-grained order-book dynamics, or any potential interactions between participants.

02Less Blurred

Formulated

Mathematical, physics (Navier-Stokes) equation-driven models generate synthetic limit-order-book data for controlled experiments under different market conditions. This centralised approach has lower granularity than fine-grained historical observations. Rayleigh Research advances this approach with Buoyancy, which models the market as a fluid.

Explore Buoyancy by Rayleigh ResearchRayleigh Ecosystem

Resolved

03Resolved

AlgoStakes® Framework

AlgoStakes® is Rayleigh’s historical order-book reconstruction and simulation technology and research framework. It uses fine-grained, high-frequency historical limit-order-book data for market reconstruction, algorithm evaluation, risk analysis, and basic market-impact analysis. Its centralised approach has limitations when representing interactions between agents.

Rayleigh Ecosystem

04Fully Resolved

Decentralised Agent-Based Modelling

The framework explores how independently operated trading agents could interact within open networks under defined incentive mechanisms. Simulated environments can expose modelled participant actions and interactions, supporting investigation of trading algorithms and market impact within the assumptions and limits of the simulation.

Rayleigh Ecosystem

Up next in Our ApproachThe Sequence MattersWhy market-by-order data matters

THE SEQUENCE MATTERS

Why Market-by-Order Data Matters

Financial markets are shaped by a continuous flow of orders, cancellations, liquidity changes, and participant interactions. Periodic snapshots capture only part of this activity. Fine-grained market-by-order data preserves more of the sequence, supporting detailed market reconstruction, simulation, trading-algorithm evaluation, and risk management.

MARKET-BY-ORDER

ILLUSTRATIVE DATA

Contours: resting quantity · Labelled points: individual orders

Initial book: resting buy and sell orders, before the events.

SNAPSHOT 0

+ B4 − B4

Added, then cancelled

SNAPSHOT 2

Same book, two events between observations

A snapshot shows the order book at one moment. The event sequence reveals what changed between observations.

CORE SERVICES

What We Deliver

We develop high-frequency market simulation technologies, fine-grained financial data systems, and intelligent market mechanisms for the agentic future of decentralised finance.

Fine-Grained Market Data for AI Trading Agents

Provide highly detailed synthetic market-by-order data and historical-data analysis under applicable licences, with associated order-book reconstruction, allowing high-activity, intelligent trading strategies to be fully developed and tested.

Market Simulation and Risk Management for Trading Algorithms

Develop advanced simulation technologies and frameworks for a careful evaluation of trading strategy performance with market impact analysis and complex interdependencies between trading agents.

Optimal Market Mechanism and Incentive Design

Research and develop state-of-the-art market microstructure mechanisms to maximise market quality in the agentic era of decentralised finance trading where trading agent incentives take the central role.

Rayleigh Ecosystem

Three perspectives One market

Buoyancy, AlgoStakes®, and decentralised agent-based modelling approach market simulation from different angles. Each addresses distinct modelling needs, and together they provide complementary capabilities for exploring market behaviour, evaluating trading algorithms, and developing more realistic environments for AI agents.

BuoyancyAlgoStakes®AI Agents

Illustrative activity, not real market data, product output, or trained AI.

Architecture

Built for Market Depth and Simulation

This capability framework connects Rayleigh’s work on fine-grained market data, order-book reconstruction, high-frequency simulation, and agent-based market mechanisms. It outlines research and development directions rather than a claim that every layer is a deployed product.

Layer 01

Market Feed

Layer 02

L3 MBO Reconstruction

Layer 03

Deep HFT Engine

Layer 04

Agentic Best Execution

Layer 05

Agentic Market Making

Layer 06

Optimized Market Microstructure

Talent

Join the Team

We're bringing together engineers, researchers, and strategic thinkers to build the next generation of AI-driven technologies for digital asset markets.

Business Growth & BD Lead

Develop research and technology partnerships, commercial relationships, and strategic growth initiatives.

C++ / Rust Engineer

Build market-data processing, order-book reconstruction, and simulation infrastructure for financial research.

Quantitative Researcher

Research trading-agent behaviour, market impact, and algorithm evaluation using detailed market data and simulation.

Quantitative Trader

Connect quantitative research with practical evaluation of trading algorithms and market behaviour.

Get In Touch

Let's Start a Conversation

Choose what brings you here. The form will adapt to your enquiry and only ask for the information relevant to that conversation.

You can email to@rayleigh.re directly.