Algorithmic Trading & Order Execution

Algorithmic Trading and Order Execution

• This course covers designing, testing, and deploying automated trading strategies.
• It includes theoretical foundations, practical implementation, and regulations.

Learning Objectives

• Comprehensive understanding of algorithmic trading role in financial markets.
• Design and implement algorithmic trading strategies, like market making and arbitrage.
• Analyze and optimize order execution algorithms to minimize costs and maximize performance.
• Evaluate market microstructure impacts on trading strategies.
• Apply risk management techniques to algorithmic trading systems.
• Understand regulations governing algorithmic trading.

Course Structure

• Introduction to Algorithmic Trading
  • Algorithmic trading involves using automated systems to execute trading strategies.
  • Various types of algorithmic trading strategies exist.
  • Algorithmic trading has advantages and disadvantages.
  • Market participants in algorithmic trading have distinct motivations.
• Market Microstructure
  • Order book mechanics and price formation are important.
  • Market impact and liquidity affect trading.
  • Transaction costs and fees must be considered.
  • Market fragmentation and connectivity are relevant.
• Algorithmic Trading Strategies
  • Market Making:
    • Market making involves inventory management.
    • Quote placement strategies affect profitability.
    • Adverse selection and information asymmetry are challenges.
  • Arbitrage:
    • Arbitrage strategies include statistical, latency, and triangular arbitrage.
  • Trend Following:
    • Trend following uses moving averages and technical indicators.
    • Pattern recognition is important.
    • Risk management is crucial in trend following.
  • Execution Algorithms:
    • VWAP, TWAP, IS, and POV are common algorithms.
• Order Execution and Optimization
  • Order routing and smart order execution are critical.
  • Venue selection and order placement affect outcomes.
  • Fill probability and order aggressiveness must be balanced.
  • Transaction cost analysis (TCA) is necessary.
  • Slippage is a key consideration.
• Risk Management in Algorithmic Trading
  • Market risk and volatility must be managed.
  • Model risk and parameter selection are relevant.
  • Operational risk and system failures can occur.
  • Regulatory compliance and legal considerations are important.
• Tools and Technologies
  • Python and C++ are used for algorithmic trading.
  • Trading platforms and APIs facilitate execution.
  • Data feeds and market data providers are essential.
  • Backtesting and simulation tools are used for validation.
• Regulatory and Legal Aspects
  • Market manipulation and fraud are concerns.
  • Regulations govern high-frequency trading.
  • Order protection rules must be followed.
  • Compliance and surveillance are necessary.
• Case Studies and Applications
  • Real-world examples showcase trading strategies.
  • Analysis of both successful and unsuccessful algorithms is instructive.
  • Guest lectures from industry professionals provide insights.

Assessment

• Assignments involve practical coding to implement and test trading strategies.
• Quizzes assess understanding of core concepts.
• A midterm exam covers theoretical foundations.
• A final project is to design, implement, and backtest a novel strategy.

Required knowledge

• Basic knowledge of financial markets is needed.
• Programming concepts are required.
• Understanding of statistics and probability is necessary.

Quantitative Finance and Risk Management

• The course offers an in-depth understanding of quantitative finance and risk management techniques.
• Students apply models to price instruments, manage risk, and make investment decisions.

Learning Objectives

• Understand mathematical foundations of quantitative finance.
• Apply statistical models to analyze financial data.
• Price and hedge derivatives and fixed-income securities.
• Measure and manage market, credit, and operational risks.
• Implement risk management strategies with quantitative tools.
• Evaluate the performance of investment portfolios.

Course Structure

• Introduction to Quantitative Finance
  • Overview of quantitative finance and its applications.
  • Role of mathematical and statistical models in finance.
  • Financial data and its characteristics are examined.
  • Portfolio Theory is a foundational element.
• Probability and Statistics for Finance
  • Probability distributions are utilized in finance.
  • Hypothesis testing and statistical inference are applied.
  • Regression analysis and time series modeling are key techniques.
  • Monte Carlo simulation is a powerful tool.
• Financial Instruments and Markets
  • Equity markets and valuation techniques are covered.
  • Fixed income securities and yield curve analysis are explored.
  • Derivatives include options, futures, and swaps.
  • Commodity markets and trading are analyzed.
• Derivatives Pricing and Hedging
  • The Black-Scholes model and its extensions are studied.
  • The binomial tree model is applied.
  • Greeks and hedging strategies are implemented.
  • Interest rate derivatives are examined.
• Risk Management
  • Market Risk:
    • Value at Risk (VaR) and Expected Shortfall (ES) are measured.
    • Stress testing and scenario analysis are conducted.
    • Volatility modeling and forecasting are essential.
  • Credit Risk:
    • Credit scoring and default probability estimation are used.
    • Credit derivatives and securitization techniques are analyzed.
    • Counterparty risk and collateral management are critical.
  • Operational Risk:
    • Risk identification and assessment are key steps.
    • Risk mitigation strategies are developed.
    • Capital adequacy and regulatory compliance are important.
• Portfolio Management
  • Portfolio optimization and asset allocation are studied.
  • Performance measurement and attribution are conducted.
  • Factor models and risk-based investing are applied.
  • Alternative investments like hedge funds are explored.
• Case Studies and Applications
  • Real-world examples of quantitative finance and risk management are analyzed.
  • Financial crises and risk management failures are studied.
  • Guest lectures from industry professionals offer practical insights.

Assessment

• Assignments involve problem sets and case studies.
• Quizzes assess understanding of key concepts.
• A midterm exam covers mathematical and statistical foundations.
• The final project involves developing a quantitative model for pricing, hedging, or risk management.

Required Knowledge

• Requires calculus.
• Requires linear algebra.
• Requires probability and statistics.

Signal-to-Noise Ratio (SNR)

• Signal-to-noise ratio (SNR) compares the power of a desired signal to background noise power.
• An SNR is the ratio of signal power to noise power.
• A high SNR means that signal is stronger as compared to noise.

Definition

• SNR is defined as: $SNR = \frac{P_{signal}}{P_{noise}}$.
• $P_{signal}$ is the signal power.
• $P_{noise}$ is the noise power.

Decibel (dB) Expression

• SNR can be expressed in decibels (dB) using the formula:
• $SNR_{dB} = 10 \log_{10}(\frac{P_{signal}}{P_{noise}})$

Example

• If a signal has 10 milliwatts (mW) and noise has 1 mW:
  • $SNR = \frac{10mW}{1mW} = 10$
  • $SNR_{dB} = 10 \log_{10}(10) = 10dB$.

Interpretation

• SNR of 1:1 (0 dB) means signal power equals noise power.
• An SNR > 1:1 (0 dB) means the signal is stronger than noise.
• An SNR < 1:1 (0 dB) means the noise is stronger than the signal.

Applications

• Communications to evaluate the quality of a communication signal.
• Audio to measure the quality of an audio equipment.
• Imaging to evaluate the quality of the image.
• Science to detect weak signals in experiments.

Factors

• Various factors impact the SNR.
  • Signal Strength: Strong signal has higher SNR.
  • Noise: Lower noise increases SNR.
  • Bandwidth: More bandwidth increases noise.
  • Impedance: Incorrect impedance increases noise/reduces SNR.

Improvement

• Several techniques improve SNR.
  • Amplification increases signal power.
  • Filtering or shileding reduces noise.
  • Lowering the bandwidth reduces the noise.

Laws of Motion

• Describe how objects move in response to applied forces.

The Concept of Force

• A force is an interaction.

Inertia and Mass

• Mass:*

• Measure of resistance to motion changes from force.

• Scalar quantity with SI unit of kg.

• Inertia:*

• Tendency to resist changes in velocity.

Example

• Smaller mass has greater acceleration because it has less inertia.

Newton's First Law

• Object continues at rest/constant velocity in absence of external forces.
• Object accelerates only if a force acts on it.

Newton's Second Law

• Acceleration is proportional to net force, inversely proportional to its mass.
• $\overrightarrow{a} \propto \frac{\overrightarrow{F}{n e t}}{m} \rightarrow \overrightarrow{F}{n e t}=m \overrightarrow{a}$
• $\overrightarrow{F}{n e t}=\sum \overrightarrow{F}=\overrightarrow{F}{1}+\overrightarrow{F}{2}+\overrightarrow{F}{3}+\ldots$
• $\vec{F}$ is the net force - vector sum of all forces on an object
• $m$ is the object's mass.
• $\vec{a}$ is the object's acceleration.
• SI unit: Newton (N), which is $1 \mathrm{~N} \equiv 1 \mathrm{~kg} \cdot \mathrm{m} / \mathrm{s}^{2}$

Force Example

• Forces are shown in Newtons and calculations made

Free-Body Diagram

• A diagram showing all the forces acting on an object.

Steps to Draw a Free-Body Diagram

1. First, draw a dot representing the object.
2. Then draw each force vector acting on the object as an arrow from the dot.
3. Lastly the the length of the arrow is proportional to the magnitude of the force

Solution

• Worked example equations*

$$\begin{aligned} & \overrightarrow{F_{\text {net }}}=\overrightarrow{F_{1}}+\overrightarrow{F_{2}} \ & \overrightarrow{F_{1}}=F_{1 x} \hat{\imath}+F_{1 y} \hat{\jmath}=5.0 \cos \left(-20^{\circ}\right) \hat{\imath}+5.0 \sin \left(-20^{\circ}\right) \hat{\jmath}=(4.7 \hat{\imath}-1.7 \hat{\jmath}) N \ & \overrightarrow{F_{2}}=F_{2 x} \hat{\imath}+F_{2 y} \hat{\jmath}=8.0 \cos \left(60^{\circ}\right) \hat{\imath}+8.0 \sin \left(60^{\circ}\right) \hat{\jmath}=(4.0 \hat{\imath}+6.9 \hat{\jmath}) N \ & \overrightarrow{F_{\text {net }}}=(4.7 \hat{\imath}-1.7 \hat{\jmath})+(4.0 \hat{\imath}+6.9 \hat{\jmath})=(8.7 \hat{\imath}+5.2 \hat{\jmath}) N \end{aligned}$$

Equations Plugged into Newton's Second Law:

$$\begin{aligned} \overrightarrow{a} &=\frac{\overrightarrow{F_{n e t}}}{m}=\frac{(8.7 \hat{\imath}+5.2 \hat{\jmath}) N}{0.30 \mathrm{~kg}}=(29 \hat{\imath}+17 \hat{\jmath}) \mathrm{m} / \mathrm{s}^{2} \ a &=\sqrt{a_{x}^{2}+a_{y}^{2}}=\sqrt{29^{2}+17^{2}}=34 \mathrm{~m} / \mathrm{s}^{2} \ \theta &=\tan ^{-1}\left(\frac{a_{y}}{a_{x}}\right)=\tan ^{-1}\left(\frac{17}{29}\right)=30^{\circ} \end{aligned}$$

Gravitational Force and Weight

• Any two objects attract each other with a gravitational force: $F_{g}=G \frac{m_{1} m_{2}}{r^{2}}$
• $G=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}$ is the gravitational constant
• $m_{1}$ and $m_{2}$ are the masses of the two objects
• $r$ is the distance between their centers
• When one of the objects is Earth: $F_{g}=G \frac{m M_{E}}{R_{E}^{2}}=m g$
• $M_{E}=5.98 \times 10^{24} \mathrm{~kg}$ is the mass of the Earth
• $R_{E}=6.37 \times 10^{6} \mathrm{~m}$ is the radius of the Earth
• $g=9.80 \mathrm{~m} / \mathrm{s}^{2}$ is the acceleration due to gravity on Earth
• Weight Magnitude of gravitational force acting on an object: $W=m g$
• Scalar quantity.
• SI unit: N
• Weight depends on $g$, so varies by location. Mass stays the same location.