Algorithmic Trading: Strategy & Development

Algorithmic Trading Development Process

• The first step involves formulating an investment strategy based on research or experience, such as statistical arbitrage.
• Backtesting utilizes historical data to validate the strategy's performance across varying market conditions and optimize parameters.
• Paper trading involves testing the strategy in a live market environment using simulated capital to identify potential bugs.
• Live trading starts with deploying the strategy using a small amount of real capital.
• Gradually increase capital if the strategy shows consistent profitability while closely monitoring performance.

Important Considerations

• Overfitting must be avoided.
• Transaction costs which include commissions must always be factored in.
• Market impact must be considered, large orders can affect the market price.
• Risk management is essential.
• Set stop loss and take profit levels
• Regulations of the market need to be adhered to.

Common Algorithms

• Moving Average Crossover involves buying when a short-term moving average surpasses a long-term one and selling when it falls below.
• Pairs Trading capitalizes on the convergence of prices between historically correlated stocks when their correlation weakens.
• Arbitrage exploits price discrepancies across different markets.
• Mean Reversion anticipates prices returning to their average level.
• Trend Following involves buying during an upward price trend and selling during a downward trend.

Risk Management Tools

• Stop Loss minimizes losses by automatically selling an asset when it hits a defined price.
• Take Profit locks in profits by automatically selling an asset when it reaches a predetermined price.
• Position Sizing involves strategically determining capital allocation for each trade.
• Diversification reduces risk by spreading investments across various assets.
• Hedging uses financial instruments to offset the potential harm of adverse price movements.
• Volatility measures the dispersion of returns for a security or market index.
• High volatility indicates a riskier security, often quantified by standard deviation or variance in returns.

VAR (Value at Risk)

• Value at Risk, or VaR, measures the potential loss in value of an asset or portfolio over a specific period and confidence level.
• A portfolio having a one-day VaR of $1 million at a 95% confidence level, means there's a 95% chance losses won't exceed $1 million in a day.

Sharpe Ratio

• The Sharpe ratio assesses risk-adjusted return, calculated using the formula: Sharpe Ratio = (Rp - Rf) / σp.
• Rp is the return of the portfolio.
• Rf is the risk-free rate.
• σp is the standard deviation of the portfolio's excess return.
• A higher Sharpe ratio signifies a more favorable risk-adjusted return.

Backtesting Key Steps

• Collect data for the assets to be traded.
• Implementing a trading strategy using code.
• Evaluate performance of strategy considering metrics.
  • Total return = profit or loss generated by the strategy.
  • Win Rate = percentage of profitable trades.
  • Maximum drawdown = max loss from peak to trough.
  • Sharpe ratio = measure of risk-adjusted return.

Walkforward Optimization

• Walkforward optimization refines backtesting by dividing historical data into periods.
• First optimize the strategy on the first period, then test during the second period.
• Repeat this process for each period.
• The results are then averaged to get an estimate of performance.
• Walkforward optimization reduces overfitting, which may result in over optimization.

Chapter 1: What is Machine Learning?

• ML programs computers to learn from data.
• Arthur Samuel: ML is the field of study that gives computers the ability to learn without being explicitly programmed.
• Tom Mitchell: A computer program is said to learn from experience E with respect to some task T and some performance measure P.
• Performance at T, as measured by P, improves with experience E.

Why use Machine Learning?

• Overcomes problems requiring manual tuning or long rules.
• Tackles complex issues lacking traditional solutions.
• Adapts to fluctuating environments with new data.
• Obtains insights from complex problems and vast datasets.

Types of Machine Learning Systems

• Supervision uses 4 different methods
  • Supervised learning: Model trained with labeled data
    • Classification predicts a category.
    • Regression predicts a value
  • Unsupervised learning: Model trained with unlabeled data.
    • Clustering groups similar instances together.
    • Anomaly detection identifies unusual events.
    • Dimensionality reduction simplifies data preserving key info.
  • Semi-supervised learning: Model trained with partially labeled data.
  • Reinforcement learning: Model trained with a reward function.
• On-Line or Batch learning uses 2 methods
  • Batch learning: Trained with all available data at once.
  • Online learning: Trained incrementally as new data arrives.
    • "Learning rate" indicates how a model adapts to new data
    • Good for continuous data streams or very large datasets
  • Out-of-core learning: Online learning system using mini-batches.
• Instance-Based vs. Model-Based
  • Instance-based learning: Learning by storing data and generalizing to new instances using a similarity measure.
  • Model-based learning: Building a model from data and using it for predictions.

Main Challenges of Machine Learning

• Bad Amount of Data
  • Insufficient Quantity of Training Data may occur.
  • Nonrepresentative Training Data like Sampling bias occur.
  • Poor quality data due to missing values, outliers, and noise.
• Bad Data
  • Irrelevant Features:
    • Feature selection.
    • Feature extraction.
    • Creating new features by gathering new data.
• Overfitting the Training Data
  • Constrain a model to make it simpler.
  • Reduces the risk of overfitting.
• Underfitting the Training Data by
  • Selecting a more powerful model.
  • Feeding better features to the learning algorithm.
  • Reducing the constraints on the model.

Testing and Validating

• Data Split:
  • Training set.
  • Test set.
• Generalization error: Error rate on new cases

Hyperparameter tuning and model selection

• Cross-validation: Split the training set into several subsets and train the model on each combination of subsets and test it on the remaining subset.

Razones para estimar el esfuerzo

• Determining project feasibility is achieved.
• Budgets and chronogram are created realistically.
• Project risks are anticipated and minimized.
• Informed decisions on project scope, resources, and quality are considered.
• Project progress is tracked and controlled.
• Accountability and communication with stakeholders is improved.

Factores que afectan la exactitud de las estimaciones

• The amount of the project, larger projects are more difficult to estimate due to complex uncertainty.
• Project Complexity with complicated and intrincate requirements.
• Project team experience with knowledge of estimation activities.
• Time Pressure may lead to hasty estimations.
• Changes in Project requirements may need reestimation.
• Assumptions and limitations must be clearly identified and documented.
• organizational biases that may influence estimates.

Técnicas de estimación

• Relying on the expertise of domain and project estimating.
• Analogous Estimation includes historical data to compare to current project.
• Parametric Estimation establishes a relation between project and effort.
• Bottom Up Estimation requires the project in smaller tasks.
• Three-point Estimation calculates a weighted estimate.
  • Triangular Distribution E = (O + M + P) / 3
  • Beta (PERT) Distribution E = (O + 4M + P) / 6
  • E is estimated.
  • O is optimistic.
  • M is the most likely.
  • P is pessimistic.
• The Monte Carlo Simulation uses multiple simulations of the project.
• COCOMO(Constructive Cost Model) estimates software development costs.
• Function points estimates the software size based on the functionality.

Consejos para mejorar la exactitud de las estimaciones

• Involve the project team in the estimating process.
• Document assumpions.
• Utilize estimation and software tools for aid.

1. Définitions

1. Espace vectoriel

• A vector space E with two operations:
• Addition: $E \times E \rightarrow E, (u, v) \mapsto u + v$
• Scalar multiplication:$K \times E \rightarrow E, (\lambda, u) \mapsto \lambda u$
• Has properties such as:
  • Associativity : $(u + v) + w = u + (v + w), \forall u, v, w \in E$
  • Neutral element: $\exists 0 \in E$ where $u + 0 = u, \forall u \in E$
  • Opposite element $\forall u \in E \exists -u \in E$ where $u + (-u) = 0$
  • Commutativity: $u + v = v + u, \forall u, v \in E$

2. Sous-espace vectoriel

• A subset F of vector space E is a vector subsapce of E if:
• F is not empty.
• F is a stable addition : $\forall u, v \in F, u + v \in F$
• F is sable by scalar multiplation: $\forall \lambda \in K, \forall u \in F, \lambda u \in F$.

3. Familles de vecteurs

• Linear combination: A combination of $v_1, v_2,..., v_n \in E$ is a vector of form $\lambda_1v_1 + \lambda_2v_2 +... + \lambda_nv_n$, where $\lambda_1, \lambda_2,..., \lambda_n \in K$.
• Generating Family: A family of vector $(v_1, v_2,..., v_n)$ is generating if any vector of E can be written as linear.
• Free Family: A family of vector ($v_1, v_2,..., v_n$) is free (or linearly independent) if:
  • $\lambda_1v_1 + \lambda_2v_2 +... + \lambda_nv_n = 0 \Rightarrow \lambda_1 = \lambda_2 =... = \lambda_n = 0$
• Base: A base of E is any family of vectors that are both free and generating.
• Dimension: The dimension of the vector can be found in the number of vectors.

2. Applications linéaires

• An application liner is an application $f : E \rightarrow F$ between two vector spaces E and F.
• Such that $f(u + v) = f(u) + f(v), \forall u, v \in E$.
• $f(\lambda u) = \lambda f(u), \forall \lambda \in K, \forall u \in E$

2. Propriétés

• $f(0_E) = 0_F$
• $f(-u) = -f(u), \forall u \in E$
• $f(\sum_{i=1}^{n} \lambda_i u_i) = \sum_{i=1}^{n} \lambda_i f(u_i)$

3. Noyau et image

• Ker(f) is a vector in $f(u) = 0_F$
• Im(f) is in F if its the vector image of in at least one vector E.

4. Rang

• Rg(f) or rank of f is a dimension of an image od f.
• If E is an dimension finite, dimension.

6. Injectivité, surjectivité, bijectivité

• f is injective if and only if $ker(f) = {0_E}$
• f is surjective if and only if im(f) = F
• f is bijective if and only if f is injective and surjective.

3. Matrices

• Matrix a table of numbers
• If two matrix A and B same M x N, its is $(A + B){ij} = a{ij} + b_{ij}$.
• Matrix and a scalar Lambda becomes $(\lambda A){ij} = \lambda a{ij}$.
• The product of two M xN matrix is C, therefore it is Mp + $c_{ij} = \sum_{k=1}^{n} a_{ik} b_{kj}$.
• Identity Matrix includes a with is 1 on diagonal and rest is 0.

2. Représentation matricielle d'une application linéaire

• An affine vector can be represented by f with a matrix A in relation.

3. Changement de base

• Changing a base is to represent the coordiantes of a vector with new base relation to the old base. 3## 4. Déterminants

• Associate a non-zero scaler that is noated det(A)

• Determine Matrix: Determinant of matrix is non inversible

• $det(AB) = det(A)det(B)$

• $det(A^T) = det(A)$

• Multiplicaiton can change sign.

3. Calcul du déterminant

• If 2 x2, this may occur $A = \begin{pmatrix} a & b \ c & d \end{pmatrix}, det(A) = ad - bc$

Diagonalisation

If $\lambda v$, v being not nul

Introduction

This paper examines the impact of order book events on algorithmic trading strategies. Algorithmic trading uses computer programs to execute orders based on pre-defined instructions. Order book events, such as limit orders, market orders, and cancellations, provide valuable information about market dynamics.

Types of Order Book Events

• Limit Orders = buy or sell at a specified price or better
• Market order = buy or sell immediately at the best available price.
• Cancellations = Removal of previously placed limit orders.

Impact of Order Book Events

• Price Discovery using supply an demand dynamics
• Liquidity insight into the available level between prices.

Types of Algorithmic Trading Strategies

• Market Making by providing to liquidity by pricing orders.
• Arbitrage capitalizing on the in efficiences.
• Trend Following identifies and capitalizes

Incorporating Order Book Events into Algorithmic Trading

• Real time allows algorithimic to trade with better info.
• Predictive modelling such as Machine Learning Techniques.
• Assessing risks of trading.
• Methodology -Data to the amount of Trading Data and order book.
  • Implemented Strategies with or without.
  • Evaluation Metrics

Results

Results show the improved the data.

La tensión se mide en newtons (N) en el Sistema Internacional de unidades (SI) o comúnmente en libras (lb)

¿Qué es la tensión?

La tensión se define como la fuerza de tracción ejercida axialmente por medio de una cuerda, cable, cadena o objeto similar, o por cada sección de un cuerpo continuo sobre la sección contigua a través de la misma. La tensión es una fuerza de "tracción". Intenta tirar de los objetos unidos a la cuerda. Debemos observar los ejemplos siguientes.

Ejemplo 1

En el primer caso, considere un bloque que está siendo jalado por una cuerda (o cable) como se muestra en la figura, la tensión es la fuerza transmitida a través de la cuerda de un extremo a otro.

Ejemplo 2

En el segundo caso, considere un bloque colgado de una cuerda (o cable) como se muestra en la figura, la tensión es la fuerza transmitida a través de la cuerda de un extremo a otro.

Ejemplo 3

En el tercer caso, considere el sistema que se muestra en la figura, donde dos bloques están conectados por una cuerda. La tensión es la misma en toda la cuerda. Esto significa que la tensión que tira del bloque 1 es de la misma magnitud que la tensión que tira del bloque 2.

Chapter 1. Introduction

• Chemical engineering thermodynamics is the application of thermodynamics to chemical processes.

1.1 Importance of Thermodynamics

• Thermodynamics ensures design of efficient and safe chemical processes.
• Maximizing yield.
• Thermodynamics troubleshoots problems in chemical processes.

1.2 Basic Concepts

• A system is a region of space that is being studied.
• Surroundings are outside the system.
• Boundary is the interface between the system and the surroundings.
• State of a system is defined by its properties.
• Process is the change in the state of the system.
• Equilibrium is a state in which there is no net change in the system.

1.3 Properties of Matter

• Intensive properties are independent mass.
• Extensive properties depend on the amount of mass.
• Specific Properties per unit mass.

1.4 Thermodynamic Laws

• Zeroth Law of Thermodynamics of two systems are equal to each other.
• First Law of Thermodynamics;
• Second Law of Thermodynamics. $\Delta S \geq 0$
• Third Law of Thermodynamics.

1.5 Thermodynamic Processes

• Isothermal Process that are constant in temp
• Isobaric Process is constant in pressure.
• Isochoric Process is constant in volume.
• Adiabatic Process
• Reversible Process can be reversed.
• Irreversible Process cannot be reversed

1.6 Applications of Thermodynamics

• Power Generation used optimixe power plants
• Refrigeration is ised to optimize systems.
• Chemical Reactions is used to to predict chemical reactions
• Phase Equilibria predicting mixtures.

Chapter 2. Volumetric Properties of Pure Fluids

2.1 Ideal Gas Law

• Ideal gases equal: $PV = nRT$