Algorithmic Trading and Order Execution

Algorithmic Trading and Order Execution

Automated Trading System

• Buy Side:
• Portfolio managers make investment decisions.
• Order generation involves deciding the quantity of shares to buy or sell.
• The Order Management System (OMS) sends orders, and tracks their status.
• Sell Side:
• The Execution Algorithm breaks orders into smaller parts to execute.
• Direct Market Access (DMA) sends orders directly to the exchange.
• Smart Order Routers (SOR) direct orders based on best execution venues.
• Feedback occurs when execution information returns to the OMS.

Order Types

• Market Order: Executes immediately at the best available price, providing certainty of execution but low price certainty, and takes liquidity.
• Limit Order: Executes at a specific price or better, delivering high price certainty but low execution certainty, and provides liquidity.
• Stop Order: Converts to a market order when a specified price is reached.
• Stop-Limit Order: Converts to a limit order when a specified price is reached.
• Market-Not-Held Order: Grants the broker discretion to execute at the best price.
• Hidden Order (Iceberg Order): Displays only a portion of the order to the market.

Order Instructions

• Day Order: Valid only for the day submitted and gets canceled at the end of the trading day if not filled.
• Good-Till-Cancelled (GTC): Remains active until filled or canceled by the investor.
• Immediate-or-Cancel (IOC): Any portion not immediately filled is cancelled.
• Fill-or-Kill (FOK): The entire order must be executed immediately and entirely, or it is cancelled.
• All-or-None (AON): Entire order must be executed, but not necessarily immediately.

Algorithmic Trading Motivations

• Reduced transaction costs are realized through automation reducing manual intervention.
• Improved execution price results from algorithms finding better prices by analyzing market data.
• Increased trading speed allows algorithms to react quickly to capture short-term opportunities.
• Order anonymity prevents front-running by hiding the trader's identity.
• Exploratory analysis is used to discover and test new trading strategies for profitability.
• Automated hedging and rebalancing adjusts portfolio positions automatically in response to market changes.

Algorithmic Trading Strategies

• Volume-Weighted Average Price (VWAP): Executes at the day's VWAP by estimating expected volume and trading proportionally: $VWAP = \frac{\sum_{i=1}^{n} P_i \times V_i}{\sum_{i=1}^{n} V_i}$
• Time-Weighted Average Price (TWAP): Divides and executes orders in slices at regular intervals to achieve the TWAP over a period.
• Implementation Shortfall: Aims to minimize the difference between the execution price and the decision price: $Implementation Shortfall = (P_E - P_D) \times N - Costs$
• Percentage of Volume (POV): Trades at a specified percentage of the total market volume by monitoring market activity.
• Dark Strategies: Use dark pools or hidden orders to execute large orders discreetly.
• Smart Order Routing: Routes orders to venues most likely to fill them at the best price using market data analysis.
• Statistical Arbitrage: Exploits mispricing between related assets, trading to profit from these inefficiencies.
• High-Frequency Trading (HFT): Uses high-speed technology to exploit short-term market inefficiencies.

Order Execution

• Upstairs Market: Involves trading large orders between dealers or institutions, typically through negotiation.
• Downstairs Market: Involves trading smaller orders on exchanges or automated systems, characterized by transparent prices.

Specialist System

• Specialists act as both brokers (agents) and dealers (principals).
• They maintain a fair and orderly market, matching buy and sell orders.
• They provide liquidity to offset temporary imbalances.

Order Precedence Hierarchy

• Price: Orders with the best price get priority.
• Time: Earlier orders take precedence.
• Size: Larger orders may take precedence.
• Display: Displayed orders may take precedence over hidden orders.

Illegal Activities

• Quote stuffing is flooding the market with immediately-cancelled orders to create confusion.
• Order anticipation is detecting a large order and trading ahead of it, only illegal with fiduciary duty.
• Trading ahead is trading for one's own account before fulfilling a client's order.

Heat Equation

Derivation

• Amount of heat energy in region $\Omega$ is $E(t) = \int_\Omega e(x, t) dx$, where e = thermal energy density.
• Rate of change of heat energy is $\frac{dE}{dt} = \int_\Omega \frac{\partial e}{\partial t} dx$.
• Heat flux, $q(x, t)$, is rate of heat energy flow per unit area, and is a vector in direction of flow.
• Heat flow out of $\Omega$ across boundary $\Gamma$ per unit time: $\int_\Gamma q \cdot n ds = \int_\Omega \nabla \cdot q dx$ via divergence theorem.
• Heat generated inside $\Omega$ by a source given by $\int_\Omega f(x, t) dx$, where f = heat source density.
• Change in heat energy equation: $\frac{dE}{dt} = -\int_\Gamma q \cdot n ds + \int_\Omega f(x, t) dx$.
• $\int_\Omega \frac{\partial e}{\partial t} dx = -\int_\Omega \nabla \cdot q dx + \int_\Omega f(x, t) dx$.
• $\int_\Omega \frac{\partial e}{\partial t} + \nabla \cdot q - f dx = 0$.
• $\frac{\partial e}{\partial t} + \nabla \cdot q - f = 0$.
• Fourier's law states heat flux is proportional to temperature gradient: $q = -k \nabla u$ (u=temperature, k=thermal conductivity).
• Thermal energy density is proportional to temperature: $e = c\rho u$ (c=specific heat, $\rho$=density).
• Substitution results in: $c\rho \frac{\partial u}{\partial t} - \nabla \cdot (k \nabla u) = f$.
• If k is constant: $c\rho \frac{\partial u}{\partial t} - k \Delta u = f$.
• $\frac{\partial u}{\partial t} - \kappa \Delta u = \tilde{f}$, where $\kappa = \frac{k}{c\rho}$ (thermal diffusivity), $\tilde{f} = \frac{f}{c\rho}$.
• This is the heat equation.

Boundary conditions

• Dirichlet boundary condition: $u(x, t) = g(x, t), x \in \Gamma$.
• Neumann boundary condition: $-k \nabla u(x, t) \cdot n = h(x, t), x \in \Gamma$.
• Robin boundary condition: $-k \nabla u(x, t) \cdot n + \alpha(x, t) u(x, t) = h(x, t), x \in \Gamma$.

The Importance of Accuracy in AI Transcription

Introduction

• Accuracy is a critical factor influencing AI transcription's usability and reliability in various fields.

Impact of Accuracy on Various Applications

• Legal Sector: demands precise documentation in court proceedings, depositions, and legal contracts.
• Medical Field: necessitates accurate patient records, diagnoses, and treatment plans to ensure patient safety.
• Business and Finance: relies on precise transcriptions of meetings, calls, and reports.
• Academic Research: accurate interview and lecture transcriptions are needed for analysis.

Factors Affecting Accuracy in AI Transcription

• Audio Quality: Background noise and poor equipment hinder accurate transcription.
• Accent and Dialect: AI models may struggle with accents and dialects.
• Technical Jargon: Specialized terminology can pose challenges for AI.
• Speaker Overlap: Multiple speakers can confuse AI transcription models.

Measures to Ensure Accuracy in AI Transcription

• High-Quality Audio Recording: Minimizes background noise and maximizes clarity.
• Training Data Optimization: Diverse datasets enhance AI models' ability to handle different speech variations.
• Human Review and Editing: Reduces errors and clarifies ambiguous passages.
• Customized Language Models: Improve understanding and transcription of technical jargon.

Conclusion

• Accuracy is paramount in usability and reliability across various applications.
• Factors such as audio quality, accents, technical jargon, can affect transcription accuracy.
• High-quality audio recording, training data optimization, human review, can ensure high-quality results to maximize benefits of AI transcription technology.

IFT 371 Analyse et conception d'algorithmes - Devoir 1

Question 1: Analyse de complexité

• Algorithm takes a table A of n non-zero positive integers as input.
• Calculates a sum based on values in the table.

Question 2: Diviser-pour-régner

• Write algorithm in pseudo-code that takes n number integers and returns the sum of table elements.

Question 3: Algorithmes de tri

• Algorithm of choice that works $O(n \log n)$
• Present the pseudo-code of your algorithm and explain how it works.

Question 4: Programmation dynamique

• Provide a dynamic programming algorithm that finds minimal coins with values representing available coins, and finds the minimal number of coins.

The Laws of Thermodynamics

Zeroth Law

• If two systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.

First Law

• Energy can neither be created nor destroyed; it can only change forms; net heat supplied = net work done; $\Delta U = Q - W$.

Second Law

• Entropy of an isolated system increases to a maximum at equilibrium; heat cannot flow spontaneously from cold to hot; the universe's entropy increases.

Third Law

• As temperature tends to absolute zero, system entropy approaches a minimum/zero, impossible to to reach in finite steps; perfect crystals at absolute zero have zero entropy.

Applications

• Zeroth: thermometers in thermal equilibrium reflect accurate readings.
• First: engines convert heat into work; refrigerators move it from cold to hot.
• Second: Heat engines' efficiency, direction of time, and irreversible processes.
• Third: understanding material behavior at low temperatures; reaching absolute zero.

Algèbre linéaire

4.1 Définitions

• An $\mathbb{R}$ vector space E with the two operations +, and $\cdot$
• $(E,+)$ meets certain criteria in order to be true

4.2 Exemples fondamentaux

• $(\mathbb{R}^n)$ with values existing between 0 and R is a vector space
• $(\mathbb{C}^n)$ with values existing between 0 and $\mathbb{C}$ is a vector space
• $\mathbb{R}[X]$ is the space of polynomials with real coefficients.
• $\mathcal{C}^0([a,b],\mathbb{R})$ is the space of contisuous functions with in $\mathbb{R}$
• $\mathcal{M}_{n,m}(\mathbb{R})$ the space of matrices is a vector space

4.3 Sous-espaces vectoriels

• Soit E un $\mathbb{R}$-espace vectoriel.
• Under certain conditions, the vector space can meet Proposition 4.3 to be true

Reglas de Inferencia

• An inference rule is a scheme for contructing valid arguments
• These rules allow us to derive logical conclusions from premises

Reglas de Inferencia Proposicionales

• Modus Ponens (MP)
• Form:
• $P \rightarrow Q$, $P$, $\therefore Q$
• Description:
• If we have that P implies Q, then we can assume Q is true
• Modus Tollends (MT)
• Form:
• $P \rightarrow Q$, $\neg Q$, $\therefore \neg P$
• Description:
• If we have that P implies Q, and Q is false, then we can asume P must be false
• Silogismo Hipotético (SH)
• Form:
• $P \rightarrow Q$, $Q \rightarrow R$, $\therefore P \rightarrow R$
• Description:
• If P implies Q and Q implies R, then P implies R
• Silogismo Disyuntivo (SD)
• Form:
• $P \vee Q$, $\neg P$, $\therefore Q$
• Description:
• If P or Q is true, and P if false Q has to be true
• Adición (ADD)
• Form:
• $P$, $\therefore P \vee Q$
• Description:
• If P is true, ther P or any proposition Q is true
• Simplificación (SIMP)
• Form:
• $P \wedge Q$, $\therefore P$
• Description:
• If P and Q are true, then P is true
• Conjunción (CONJ)
• Form:
• $P$, $Q$, $\therefore P \wedge Q$
• Description:
• If P and Q are true, then P and Q are true
• Dilema Constructivo (DC)
• Form:
• $(P \rightarrow Q) \wedge (R \rightarrow S)$, $P \vee R$, $\therefore Q \vee S$
• Description:
• If P implies Q and R implies S, and P or r is true, then Q or S is true

Reglas de Inferencia Cuantificacionales

• Descripción:
• Rules that are fundamental to constructing arguments
• Examples
• Formulas shown to define a valid point
• Descriptions further elaborate what the forms mean at a high level

Lecture 18: Brain and Cognition I

Main Points

• Neurons communicate through electrical, chemical, and distinct brain areas.
• Brain imaging techniques offer perception of brain acitivity and structure.

Neurons

• Form building block of nervous system, contains cell bodies and axons
• Types: Interneurons, sensory and motor

Neural Communication

• Neurons communicating from rapid change in electric field to membrane potential

Brain Organization

• Largest part of the brain is Cerebrum, composed of hemispheres, and different lobes
• Other sections include the Limbic System, Hemispheric Specialization,

Brain Imaging Techniques

• Electroencephalography (EEG)
• Magnetoencephalography (MEG), Computed Tomography (CT)
• Magnetic Resonance Imaging (MRI) and functional
• Positron Emission Tomography (PET)

Resumen Ejecutivo

Introducción

• An investment opportunity is being presented
• The opportunity lies in the food processing plant
• This would provide an food ammount to the local animals
• The growth, the demand

Análisis del Mercado

• The market would be growing an amount and not enough for the people in the region
• More producers understand alimentation

Descripción del Proyecto

• The project is to install a processing plant
• Infrastructure for a food area
• Stages of the projects are described

Inversión y Financiamiento

• Total investments is about 2,500,000 USD
• Finance would be provided by bank lending and personal use money

Rentabilidad del Proyecto

• Project expects annual income
• Indicators include:
• Returns
• Value
• Recovery of periods

Conclusiones

• Contributes economic growth to the region
• Contributes a means of livelihood for producers
• The economic profitability is solid
• The economy is likely to do well
• These opportunities exist within the area

Explore algorithmic trading systems: buy-side order generation and sell-side execution algorithms. Understand market, limit, and stop orders, their execution certainty, and liquidity impact. Learn about Direct Market Access (DMA) and Smart Order Routers (SOR).