Algorithmic Trading Explained

Algorithmic Trading

• Algorithmic trading employs algorithms to execute trades based on identified opportunities.
• Quantitative trading uses mathematical and statistical analysis to find trading opportunities.
• Machine learning algorithms, like neural networks and decision trees, identify patterns and predict price movements.
• Natural Language Processing (NLP) analyzes text data (news, social media) to gauge sentiment and forecast market trends.
• Data is sourced from financial data providers (Bloomberg, Reuters), news outlets, social media, and economic indicators.
• Risk management is crucial due to the complexity of algorithmic strategies. Techniques include stop-loss orders, position sizing, diversification, and stress testing.
• Regulatory compliance is essential when engaging in algorithmic trading.
• Backtesting assesses strategy performance on historical data for evaluation and risk identification.
• Paper trading tests strategies in a simulated environment before risking actual capital.
• Deployment involves putting a trading strategy into live operation.
• Continuous monitoring is needed to spot strategy issues and adjust accordingly.
• LUCAS PAPADIMITRIOU describes the Internet as an algorithmic game

Algorithmic Game Theory

• Game theory seeks to explain strategic interactions among agents, where one agent's actions affect others' utilities.
• Algorithmic Game Theory incorporates computational constraints into game theory. It considers agents abilities to make calculations.
• Selfish Routing: Agents choose paths to minimize latency caused by congestion in a network. Traffic occurs, everyone acts as the network directs.
  • The Price of Anarchy measures the ratio of the cost at Wardrop equilibrium to the optimal system cost.
• Mechanism Design aims to create games with desirable outcomes, even in the presence of private information.
  • The VCG mechanism maximizes the sum of reported valuations and is truthful.
• Reading material can be found in "Algorithmic Game Theory", Nisan, Roughgarden, Tardos, Vazirani, Cambridge University Press, 2007 and "Twenty Lectures on Algorithmic Game Theory", Roughgarden, Cambridge University Press, 2016.

Linear Algebra: Determinants

• Determinants are scalar values ​​associated with square matrices and can be written det(A) or |A|.
• The determinant of a 2x2 matrix [[a, b], [c, d]] equals ad - bc.
• The determinant of a 3x3 matrix [[a, b, c], [d, e, f], [g, h, i]] equals a(ei - fh) - b(di - fg) + c(dh - eg).
• Properties include: zero determinant for matrices with zeroed/identical rows/columns; sign change upon row/column swap; scalar multiplication effects; determinant invariance under row addition.
• A square matrix A is invertible if and only if det(A) != 0.
• Cramer's Rule uses determinants to solve linear systems.

Chemical Kinetics

• Reaction rate measures the change in reactant or product concentration over time, typically in mol L-1 s-1.
• Rate laws relate reaction rates to reactant concentrations: Rate = k[A]^m[B]^n.
• Integrated rate laws relate reactant concentration to time.
• Three orders of reaction can occur: First, Second, Zero.
• Collision theory states, reactions occur when molecules collide with proper energy and orientation.
• The Arrhenius Equation describes the relationship between the rate constant, temperature, and activation energy: k = Ae-Ea/RT.
• Reaction mechanisms describe the step-by-step pathway from reactants to products, with the slowest (rate-determining) step controlling the overall reaction rate.
• Heterogeneous catalysis involves a different substance being introduced during the process to facilitate the reaction to occur faster.
• Enzymes accelerate biological reactions through specific substrate binding at the active site.

Thermodynamics

• The first law of thermodynamics expresses conservation of energy: ΔU = Q - W.
• Isovolumetric processes: no change in volume, ΔU = Q.
• Isobaric processes: constant pressure, W = PΔV.
• Isothermal processes: constant temperature, Q = W.
• Adiabatic processes: involve no heat exchange, ΔU =-W.
• Efficiency of heat engines: e = W/QH = (QH - QC)/QH = 1 - QC/QH.
• Carnot efficiency gives the maximum possible efficiency: e_max = 1 - TC/TH, with temperatures in Kelvin.
• Second Law: The entropy (S) of the isolated system can only increase
• Reversible process: ΔS = 0
• Irreversible process: ΔS > 0

MongoDB Quick Start Guide

• MongoDB is a NoSQL document database characterized by its open-source, cross-platform nature, schema flexibility, and high scalability.
• Key Benefits: document orientation, dynamic schema, high availability, escalabity.
• Basic Operations are performed on databases, collections, and documents using JavaScript syntax via the mongo shell

Algorithmic Complexity

• Algorithmic Complexity measures the resources that a computation requires for its given input size.
• Cost of computation is the time complexity, which is the number of steps/memory required.
• Asymptotic analysis: determines how the cost scales with input size.
• Asymptotic Analysis is useful but not the whole story. Measuring performance is essential in the real-world scenario.

Linear Algebra and Analytical Geometry

• Linear equations in variables x_1, x_2, ..., x_n take the form a_1x_1 + a_2x_2 + ... + a_nx_n = b where a_1, a_2,... a_n, b are constants.
• Methods for solving linear equations: Gaussian Elimination/Gauss-Jordan Elimination.

Linear Algebra

• A determinant $A \in M_n(\mathbb{K})$. is defined to be $\operatorname{det}(A)=\sum_{\sigma \in \mathcal{S}{n}} \varepsilon(\sigma) \prod{i=1}^{n} a_{i \sigma(i)}$
• Use $\operatorname{det}(A B)=\operatorname{det}(A) \operatorname{det}(B)$ to determine if an element is not invertible. Also, $\operatorname{det}\left(A^{-1}\right)=\frac{1}{\operatorname{det}(A)}$
• Cramer's rule in linear algebra uses determinant properties to solve linear equations.

Bayesian Approach to Parameter Estimation

• Bayesian approach treats parameters as random variables with probability distributions.
• Bayes Theorem updates beliefs about parameters by considering prior beliefs and observed data.