MATLAB

8-hours course

This course reviews the basics of MATLAB, which are useful to practice the Body of Knowledge of the ARPM Certificate
About the ARPM Lab
About quantitative finance: P and Q
Notation
The "Checklist": executive summary
Risk drivers identification
Equities
Currencies
Fixed-income
Derivatives
Credit
Strategies
Quest for invariance
Simple tests
Efficiency: random walk
Mean-reversion (discrete state)
Volatility clustering
Representations of a distribution
Normal distribution
Notable multivariate distributions
Elliptical distributions
Scenario-probability distributions
Exponential family distributions
Mixture distributions
Expectation and variance
Expectation and covariance
L2 geometry
Univariate results
Definition and properties of copulas
Special classes of copulas
Implementation
Multivariate quest
Order-one autoregression
Covariance stationary processes (*)
Cointegration
Estimation
Setting the flexible probabilities
Historical
Maximum likelihood
Robustness
(Dynamic) copula-marginal
Missing data
Shrinkage
Factor models and learning
Overview
Regression LFM's
Principal component LFM's
Systematic-idiosyncratic LFM's
Cross-sectional LFM's
Capital asset pricing model framework
Overview
Point vs. probabilistic statements
Inference and learning
Least squares regression
Classification
Least squares autoencoders
Probabilistic graphical models
Estimation risk assessment
Regularization and features selection
Bayesian estimation
Ensemble learning
Overview
Linear state space models
Wold representation (*)
Cramer representation
Probabilistic state space models
Wiener-Kolmogorov filtering (*)
Dynamic principal component (*)
Kriging/Gaussian processes (*)
Projection
One-step historical projection
Univariate analytical projection (*)
Efficiency: Lévy processes
Mean-reversion (discrete state)
Multivariate analytical projection
Monte Carlo
Application to credit risk
Historical
Pricing at the horizon
Exact repricing
Carry (*)
Taylor approximations
Aggregation
Stock variables
Portfolio value (*)
Credit value adjustment (*)
Liquidity value adjustment (*)
Portfolio P&L
Returns
Static market/credit risk
Dynamic market/credit risk
Stress-testing
Enterprise risk management
Ex-ante evaluation
Stochastic dominance
Satisfaction/risk measures
Mean-variance trade-off
Quantile (value at risk)
Coherent satisfaction measures
Non-dimensional ratios
Ex-ante attribution: performance
Bottom-up exposures
Top-down exposures: factors on demand
Application: hedging
Ex-ante attribution: risk
Risk budgeting: general criteria
Mean-variance principles
Benchmark allocation
Continuous programming
Integer N-choose-K heuristics
Mean-variance pitfalls
Estimation risk measurement
Robust allocation
Diversification management
Equilibrium prior
Active views
Posterior
Limit cases and generalizations
Signals
Carry signals (*)
Value signals
Technical signals
Microstructure signals (*)
Fundamental and other signals (*)
Signal processing
Simplistic portfolio construction
Advanced portfolio construction
Relationship with FLAM and APT
Multiple portfolios
Fundamental law of active management
Construction: time series strategies
The market
Expected utility maximization
Option based portfolio insurance
Signal induced strategy
Execution
High frequency risk drivers
Market impact modeling
Order scheduling
Order placement (*)
About the ARPM Lab
About quantitative finance: P and Q
Notation
The "Checklist": executive summary
Risk drivers identification
Equities
Currencies
Fixed-income
Derivatives
Credit
Strategies
Quest for invariance
Simple tests
Efficiency: random walk
Mean-reversion (discrete state)
Volatility clustering
Representations of a distribution
Normal distribution
Notable multivariate distributions
Elliptical distributions
Scenario-probability distributions
Exponential family distributions
Mixture distributions
Expectation and variance
Expectation and covariance
L2 geometry
Univariate results
Definition and properties of copulas
Special classes of copulas
Implementation
Multivariate quest
Order-one autoregression
Cointegration
Estimation
Setting the flexible probabilities
Historical
Maximum likelihood
Robustness
(Dynamic) copula-marginal
Missing data
Shrinkage
Factor models and learning
Overview
Regression LFM's
Principal component LFM's
Systematic-idiosyncratic LFM's
Cross-sectional LFM's
Capital asset pricing model framework
Overview
Point vs. probabilistic statements
Inference and learning
Least squares regression
Bias versus variance
Classification
Least squares autoencoders
Probabilistic graphical models
Estimation risk assessment
Regularization and features selection
Bayesian estimation
Ensemble learning
Linear state space models
Overview
Cramer representation
Probabilistic state space models
Projection
One-step historical projection
Efficiency: Lévy processes
Mean-reversion (discrete state)
Multivariate analytical projection
Monte Carlo
Application to credit risk
Historical
Pricing at the horizon
Exact repricing
Taylor approximations
Aggregation
Stock variables
Portfolio P&L
Returns
Static market/credit risk
Dynamic market/credit risk
Stress-testing
Enterprise risk management
Ex-ante evaluation
Stochastic dominance
Satisfaction/risk measures
Mean-variance trade-off
Quantile (value at risk)
Coherent satisfaction measures
Non-dimensional ratios
Ex-ante attribution: performance
Bottom-up exposures
Top-down exposures: factors on demand
Application: hedging
Ex-ante attribution: risk
Risk budgeting: general criteria
Mean-variance principles
Benchmark allocation
Continuous programming
Integer N-choose-K heuristics
Mean-variance pitfalls
Estimation risk measurement
Robust allocation
Diversification management
Equilibrium prior
Active views
Posterior
Limit cases and generalizations
Signals
Value signals
Technical signals
Signal processing (*)
Simplistic portfolio construction
Advanced portfolio construction
Relationship with FLAM and APT
Multiple portfolios
The market
Expected utility maximization
Option based portfolio insurance
Signal induced strategy
Execution
High frequency risk drivers
Market impact modeling
Order scheduling
About the ARPM Lab
About quantitative finance: P and Q
Notation
The "Checklist": executive summary
Representations of a distribution
Marginalization
Conditioning
Normal distribution
Quadratic-normal distribution
Notable multivariate distributions
Elliptical distributions
Scenario-probability distributions
Exponential family distributions
Mixture distributions
Expectation and variance
Expectation and covariance
L2 geometry
Univariate results
Definition and properties of copulas
Special classes of copulas
Implementation
Quest for invariance
Simple tests
Efficiency: random walk
Mean-reversion (discrete state)
Long memory: fractional integration
Volatility clustering
Multivariate quest
Order-one autoregression
VARMA processes
Wold representation (*)
Cramer representation (*)
Cointegration
Estimation
Setting the flexible probabilities
Historical
Maximum likelihood principle
Maximum likelihood
Missing data
Robustness
(Dynamic) copula-marginal
Bayesian statistics
Bayesian estimation
Factor models and learning
Overview
Regression LFM's
Systematic-idiosyncratic LFM's
Principal component LFM's
Cross-sectional LFM's
Machine learning: foundations
Overview
Point vs. probabilistic statements
Inference and learning
Least squares regression
Classification
Least squares autoencoders
Discriminant regression
Discriminant classification
Probabilistic graphical models
Overview
Least squares dynamic models
Wiener-Kolmogorov filtering
Dynamic principal component
Probabilistic state space models
Background
Foundations of decision theory
Estimation risk assessment
Regularization
Shrinkage
Sparse principal component
Ensemble learning
Time series models
Maximum likelihood
Bayesian
Mixed approach
Fit and assessment
Logistic regression
Interactions
Encoding
Regularization
Trees
Gradient boosting
Cross-validation
About the ARPM Lab
About quantitative finance: P and Q
Notation
The "Checklist": executive summary
Valuation foundations
Points of interest and pitfalls
Risk drivers identification
Equities
Currencies
Fixed-income
Derivatives
Credit
Insurance
Operations
Strategies
Projection
Efficiency: Lévy processes
Mean-reversion (continuous state)
Mean-reversion (discrete state)
Volatility clustering
Multivariate mean reversion
Multivariate analytical projection
Monte Carlo
Historical
Application to credit risk
Square-root rule and generalizations
Fundamental axioms
Stochastic discount factor
Fundamental theorem of asset pricing
Risk-neutral pricing
Capital asset pricing model framework
Covariance principle
Completeness
Arbitrage pricing theory
Intertemporal consistency
Fundamental axioms
Valuation as evaluation
Pricing at the horizon
Exact repricing
Carry
Taylor approximations
Mean-variance principles
Benchmark allocation
Optimization – overview
Convex programming
Integer N-choose-K heuristics
Sample-based allocation
Prior allocation
Bayesian allocation
Robust allocation
Diversification management
Mean-variance pitfalls
General views processing
Minimum relative entropy
Black-Litterman
Equilibrium prior
Active views
Posterior
Limit cases and generalizations
Introduction
Signals
Carry signals
Value signals
Technical signals
Microstructure signals
Fundamental and other signals
Signal processing
Simplistic portfolio construction
Advanced portfolio construction
Fundamental law of active management
Relationship with FLAM and APT
Multiple portfolios
Construction: time series strategies
The market
Expected utility maximization
Option based portfolio insurance
Convexity analysis
Execution
High frequency risk drivers
Market impact modeling
Order scheduling
Order placement
About the ARPM Lab
About quantitative finance: P and Q
Notation
The "Checklist": executive summary
Mean-variance principles
Benchmark allocation
Optimization – overview
Continuous programming
Integer N-choose-K heuristics
Mean-variance pitfalls
Environment and interface
Variables: arrays, numeric, logical, structures, string character arrays, cell arrays
Data handling: table, timetable, and datetime
Syntax and control structures (if-else, for loops, while loops, switch-case)
Scripts, function definition, simple classes
Optimization: intro to linear and nonlinear optimization, CVXOPT
Optimization: intro to quadratic programming
Linear algebra
Plotting
Machine learning and Neural Networks
Documentation and debugging
Notation
Derivative and chain rule (instantaneous forward rate)
Monotonicity (trading strategies in the Almgren-Chriss model)
Concavity/convexity (concavity/convexity of a satisfaction measure)
Taylor polynomial (Taylor approximations)
Integral (continuous rebalancing limit)
Fundamental theorem of calculus (transformation of a random variable)
Change of variable (derivation of the Black-Scholes- Merton formula)
Integration by parts formula (the P&L of trading strategy)
Multivariate function (representation of a distribution; multivariate cdf)
Partial derivative, directional derivative, and gradient (Derivatives; Greeks)
Iterated integral (marginalization, e.g. uniform bivariate)
Chain rule for multivariate function (Euler decomposition)
Convexity and Hessian matrix (convexity analysis)
Change of variables and Jacobian (pdf of an invertible function; pdf of a copula)
Relative extremum (mode)
Unconstrained optimization problem (mode)
Second derivative test (mean-variance trade-off)
Constrained optimization problem (linear programming; convex programming)
The method of Lagrange multipliers (views processing)
Functional (e.g. mean; variance; median; mode)
Derivative of functional (influence function; influence function of maximum likelihood estimators)
Variational problem (mean-variance optimization problem in the Almgren-Chriss model)
Euler-Lagrange equation (P&L optimization: Almgren-Chriss model)
Matrices and vectors (portfolio P&L scenarios; stochastic discount factor)
Row operations and rank of a matrix
Matrix manipulations (matrix algebra; matrix calculus)
Linear independence, spanning, and basis (market completeness)
Inverse of a matrix (pseudo-inverse)
Trace and determinant of a square matrix (properties of trace)
Eigenvalues and eigenvectors (spectral theorem; recursive solution; principal component analysis)
Diagonalization of symmetric matrices (spectral theorem example)
The Gram-Schmidt procedure (Gram-Schmidt)
Statistical features (expectation; standard deviation; mode; modal dispersion)
Notable distributions (normal; Student t; Cauchy)
Transformations (probability density function; cumulative distribution function; Lognormal)
Matrices and vectors (gradient; Hessian; expectation; covariance; mode; modal square-dispersion)
Affine transformations (Taylor expansion of characteristic function)
Positive definite matrices (covariance; modal square-dispersion)
Length, distance and angle
Multivariate case: covariance product
Geometry of portfolios
Many types of Fourier transform
Linear algebra perspective
Functional analysis perspective
Environment and interface
Variables: float, integer, string, boolean, list, tuple, numpy array
Data handling: Pandas
Syntax and control structures (if-else, for, while, break)
Functions definition, modules
Optimization: cvxopt and SciPy
NumPy and matrix decomposition
Plotting: Matplotlib (pyplot)
Documentation and debugging
Machine learning: scikit-learn
About the ARPM Lab
About quantitative finance: P and Q
Notation
The "Checklist": executive summary
Aggregation
Stock variables
Portfolio value
Credit value adjustment
Liquidity value adjustment
Portfolio P&L
Trading P&L
Implementation shortfall
Returns
Excess performance
Static market/credit risk
Dynamic market/credit risk
Stress-testing
Stress-testing in banks
Enterprise risk management
Enterprise risk management - Practice
Ex-ante evaluation
Stochastic dominance
Satisfaction/risk measures
Mean-variance trade-off
Quantile (value at risk)
Enterprise risk management
Coherent satisfaction measures
Non-dimensional ratios
Additional measures
Ex-ante attribution: performance
Bottom-up exposures
Top-down exposures: factors on demand
Application: hedging
Ex-ante attribution: risk
Risk budgeting: general criteria
Diversification management
About the ARPM Lab
About quantitative finance: P and Q
Notation
The "Checklist": executive summary
Risk drivers identification
Equities
Fixed-income
Credit
Quest for invariance
Simple tests
Efficiency: random walk
Mean-reversion (discrete state)
Expectation and covariance
Univariate results
Definition and properties of copulas
Special classes of copulas
Implementation
Estimation
Setting the flexible probabilities
Historical
Maximum likelihood
(Dynamic) copula-marginal
Factor models and learning
Overview
Regression LFM's
Principal component LFM's
Projection
Monte Carlo
Application to credit risk
Pricing at the horizon
Exact repricing
About the ARPM Lab
About quantitative finance: P and Q
Notation
The "Checklist": executive summary
Representations of a distribution
Marginalization
Conditioning
Normal distribution
Quadratic-normal distribution
Notable multivariate distributions
Elliptical distributions
Scenario-probability distributions
Exponential family distributions
Mixture distributions
Expectation and variance
Expectation and covariance
L2 geometry
Univariate results
Definition and properties of copulas
Special classes of copulas
Implementation
Quest for invariance
Simple tests
Efficiency: random walk
Order-one autoregression
Mean-reversion (discrete state)
Long memory: fractional integration
Volatility clustering
Multivariate quest
VARMA processes
Wold representation
Cointegration
Estimation
Setting the flexible probabilities
Historical
Maximum likelihood principle
Maximum likelihood
Missing data
Robustness
(Dynamic) copula-marginal
Bayesian statistics
Bayesian estimation
Factor models and learning
Overview
Regression LFM's
Systematic-idiosyncratic LFM's
Principal component LFM's
Cross-sectional LFM's
Least squares regression
Classification
Least squares autoencoders
Probabilistic graphical models
Shrinkage
Foundations of decision theory
Estimation risk assessment
Overview
Least squares dynamic models
Levinson filtering
Wiener-Kolmogorov filtering
Kriging/Gaussian processes
Dynamic principal component
Probabilistic state space models
About the ARPM Lab
About quantitative finance: P and Q
Notation
The "Checklist": executive summary
Risk drivers identification
Equities
Currencies
Fixed-income
Derivatives
Credit
Strategies
Quest for invariance
Simple tests
Efficiency: random walk
Mean-reversion (discrete state)
Volatility clustering
Representations of a distribution
Normal distribution
Notable multivariate distributions
Elliptical distributions
Scenario-probability distributions
Exponential family distributions
Mixture distributions
Expectation and variance
Expectation and covariance
L2 geometry
Univariate results
Definition and properties of copulas
Special classes of copulas
Implementation
Multivariate quest
Order-one autoregression
Cointegration
Estimation
Setting the flexible probabilities
Historical
Maximum likelihood
Robustness
(Dynamic) copula-marginal
Missing data
Shrinkage
Factor models and learning
Overview
Regression LFM's
Principal component LFM's
Systematic-idiosyncratic LFM's
Cross-sectional LFM's
Capital asset pricing model framework
Overview
Point vs. probabilistic statements
Inference and learning
Least squares regression
Classification
Least squares autoencoders
Probabilistic graphical models
Estimation risk assessment
Regularization and features selection
Bayesian estimation
Ensemble learning
Overview
Linear state space models
Cramer representation
Probabilistic state space models
Projection
One-step historical projection
Efficiency: Lévy processes
Mean-reversion (discrete state)
Multivariate analytical projection
Monte Carlo
Application to credit risk
Historical
Pricing at the horizon
Exact repricing
Taylor approximations
Aggregation
Stock variables
Portfolio P&L
Returns
Static market/credit risk
Dynamic market/credit risk
Stress-testing
Enterprise risk management
Ex-ante evaluation
Stochastic dominance
Satisfaction/risk measures
Mean-variance trade-off
Quantile (value at risk)
Coherent satisfaction measures
Non-dimensional ratios
Ex-ante attribution: performance
Bottom-up exposures
Top-down exposures: factors on demand
Application: hedging
Ex-ante attribution: risk
Risk budgeting: general criteria
Mean-variance principles
Benchmark allocation
Convex programming
Integer N-choose-K heuristics
Mean-variance pitfalls
Estimation risk measurement
Robust allocation
Diversification management
Equilibrium prior
Active views
Posterior
Limit cases and generalizations
Signals
Value signals
Technical signals
Signal processing (*)
Overview
Simplistic portfolio construction
Advanced portfolio construction
Relationship with FLAM and APT
Multiple portfolios