Programming 101

Tutors

• Programming tools in R, Python and Matlab
• User-defined functions
• Data I/O and financial providers download
• Plotting functions
• Functions for random and stochastic variables

Manuele Monti

• Time series analysis
• Returns and Normality test (+coding)
• Correlation, Co-Integration Analysis (+coding)
• Basic Stochastic processes (Random Walk, Brownian Motion, GBM, Mean Reversion)

Giordano Frezza

• Trading system process: from the idea to the automatic trading
• Data base management
• Fees: spread, market impact, brokers
• Risk and performance quantitative parameters (+ coding)
• Objective/predictor, optimization, multi objective function (+ coding)
• IN/OUT and smoothing analysis (+ coding)
• Backtesting and execution (+ coding)
• Updating and Handling Risk Management in Automated systems

Manuele Monti

• Risk Metrics, factors
• Risk models and measures (VaR, ES, CVaR, PaR, CFaR)
• Primer on risk management analytical and numerical techniques

Trend-following strategies

Giordano Frezza

• Rho analysis, time series dependence based on autocorrelation (Levich-Rizzo) (+ coding)
• Trend following trading system example (+ coding)

Simone Siragusa (2.5h)

• Volatility Modelling (+coding)
• Variance pitfalls
• Exponential smoothing
• GARCH and Leverage effect
• Realized variance
• Correlation Modelling (+coding)
• Value at risk and the needs of covariance
• Cluster analysis
• Modelling Conditional covariance and correlation
• Monte Carlo Analysis with different covariance matrixes
• Implied volatility arbitrage and the case of dispersion trading
• Correlation risk and hedge fund returns

Rocco Mosconi, Mattia Manzoni

• Kalman filter: a latent variable model applied to a systematic trading strategy
• An alternative to cointegration
• An “in house” custom solution (+ coding)
• Backtesting

Statistical Arbitrage

Ernest P.Chan (7.0h)

• Stationarity and cointegration of time series
• Stationarity and mean-reversion: the practical benefits.
• Cointegration vs correlation.
• Mean-reversion trading of pairs and triplets
• Finding hedge ratio through linear regression (LR).
• Order-dependence of hedge ratio based on LR.
• Finding hedge ratio through Johansen test.
• Case study: The breakdown of cointegration of GLD-GDX, the economic reasons and the remedy.
• Half-life of mean-reversion
• Practical importance of half-life.
• The Ornstein-Uhlenbeck formula.
• Risk management of mean-reversion strategies
• Index arbitrage
• Trading an ETF against a basket of its component stocks.
• Constructing a basket : linear regression, constrained optimization
• Long-short portfolio
• Long-short portfolio strategy of stocks in the S&P 500

Forecasting & Artificial Intelligence Based Strategies

Ernest P.Chan

• General paradigm of machine learning.
• AI techniques
• Stepwise linear regression
• Classification and regression trees (CART)
• Neural networks
• Genetic algorithm
• Bayesian networks
• Support Vector Machines (SVM)
• Predicting returns of a portfolio using stepwise linear regression, CART, neural network, and SVM (+coding)

Ernest P.Chan

• Markowitz mean-variance optimization as applied to strategies.
• Theoretical derivation of Kelly formula.
• Exercise: Testing the implications of Kelly formula.
• Exercise: Finding the optimal allocations of N strategies based on Kelly formula.
• Simpler ways to allocate leverage.
• Exercise: Experimenting with variations of the optimization scheme to achieve better out-of-sample performance.
• Portfolio Optimization

Yiran Liu (3.0h)

Introduction

• Definition of Market Maker
• Difference between Proprietary Trading and Market Making
• Let’s start a simple Market Making Shop (business Model Market Maker)
• Profit and Risk of our Business

Market Making Strategies

• Plain Market Making (Non Offset, Full Offset, Direction and Timing)
• Risk Analysis of such strategies: Adverse selection
• Other source of Market Making costs

Optimal Control Problem

• A Toy Example of optimal control
• Hamilton-Jacobi_Bellman Equation
• Feynman Kac Theorem
• Solving HUB Equation

Modelling Key Components

• Market Model
• Order Arriving Model
• Inventory Model
• Spread Model
• Utility Function
• Extend the Optimal Control Problem

Numerical Solution (+coding)

• Assemble the Component Models into a whole system
• Simulation of Client Order Arrivals and Market Dynamics
• A test of applying same model on real market price

Statistical results and analysis

• Factor analysis + coding, chart and tables

What to consider if we want to use the pure math idea into production

• May try to improve Price Model
• More sophisticated directional betting factor
• More Factors to put in to control, such as spread

Michele Bogliardi

• Propietary APIs
• APIs vs strategies (i.e. Spread Trading, HFT)
• Python, R and Matlab APIs
• Example: Matlab API in multiple Spread Trading

Antonio Lengua

• Mechanic of market volume
• From discretional to systematic trading

Rocco Mosconi, Mattia Manzoni

• Quantitative Trading Strategies based on High Frequency Data
• The leading informative content of order imbalance indicator
• The role of sampling rule with high frequency data: Time vs. Volume Clock approaches