Lab
Overview
Theory
Case studies
Simulation clips
Code
Documentation
Python
MATLAB
Exercises
Slides
Video lectures
Registration
Training
Overview
Global coverage:
Bootcamp (onsite/online)
Overview
Delivery
Program details
Bootcamp - day 1
Bootcamp - day 2
Bootcamp - day 3
Bootcamp - day 4
Bootcamp - day 5
Bootcamp - day 6
Networking
Social mixer
Gala dinner
Alumni connector
MOOC - Online
Brochure
Who is it for?
FAQ
Registration
Marathon (online)
Overview
Delivery
Program details
Mathematics
refresher
Python
refresher
MATLAB
refresher
Fin. Engineering for Investment
Data Science for Finance
Quant. Risk Management
Quant. Portf. Management
Brochure
Who is it for?
FAQ
Registration
Special topics:
Fin. Engineering for Investment
Data Science for Finance
Quant. Risk Management
Quant. Portf. Management
Refresher
- Mathematics
Refresher
- Python
Refresher
- MATLAB
Certificate
Overview
Body of knowledge
Fin. Engineering for Investment
Data Science for Finance
Quant. Risk Management
Quant. Portf. Management
Testing
Level 1 Exam
Level 2 Exam
Practical Project
How to prepare
FAQ
Registration
Pricing
Community
Membership
Discussions
Alumni
Events
Partner universities
About
Testimonials
ARPM
Advisory board
Attilio Meucci
Book
Charity
Contact
Sign in
Sign in
Home
Lab
Overview
Theory
Case studies
Simulation clips
Code
Documentation
Python
MATLAB
Exercises
Slides
Video lectures
Registration
Training
Overview
Bootcamp
Overview
Delivery
Program details
Bootcamp - day 1
Bootcamp - day 2
Bootcamp - day 3
Bootcamp - day 4
Bootcamp - day 5
Bootcamp - day 6
Networking
Social mixer
Gala dinner
Alumni connector
MOOC - Online
Brochure
Who is it for?
FAQ
Registration
Marathon
Overview
Delivery
Program Details
Refresher
- Mathematics
Refresher
- Python
Refresher
- MATLAB
Fin. Engineering for Investment
Data Science for Finance
Quant. Risk Management
Quant. Portf. Management
Brochure
Who is it for?
FAQ
Registration
Fin. Eng. for Investment
Data Science for Finance
Quant. Risk Mngt.
Quant. Portfolio Mngt.
Refresher - Mathematics
Refresher - Python
Refresher - MATLAB
Certificate
Overview
Body of knowledge
Fin. Engineering for Investment
Data Science for Finance
Quant. Risk Management
Quant. Portf. Management
Testing
Level 1 Exam
Level 2 Exam
Practical Project
How to prepare
FAQ
Registration
Pricing
Community
Membership
Discussions
Alumni
Events
Partner universities
About
Testimonials
ARPM
Advisory board
Attilio Meucci
Book
Charity
Contact
Lab
»
Overview
Theory
Simulation clips
Case studies
Code
Exercises
Slides
Video lectures
Registration
Sort by:
Topic
Most recent
Most popular
0 . Executive summary
The “Checklist” - Executive summary
1 . Risk drivers identification
The “Checklist” - Risk drivers identification
View in Lab:
Risk drivers identification
The “Checklist” - Risk drivers identification - Equities
View in Lab:
Equities
The “Checklist” - Risk drivers identification - Currencies
View in Lab:
Currencies
Exchange rates
Contracts
The “Checklist” - Risk drivers identification - Fixed-income
View in Lab:
Fixed-income
Zero-coupon bond
Rolling value
Yield to maturity
Alternative representations
Parsimonious representations
Spreads
The “Checklist” - Risk drivers identification - Derivatives
View in Lab:
Derivatives
Call option
Rolling value
Implied volatility
Alternative representations
Parsimonious representations
Pure volatility products
The “Checklist” - Risk drivers identification - Credit
View in Lab:
Credit
Obligor-level risk drivers
Aggregate risk drivers
Structural models
The “Checklist” - Risk drivers identification - Insurance
View in Lab:
Insurance
The “Checklist” - Risk drivers identification - High frequency
View in Lab:
High frequency
Market microstructure
Activity time
Time-changed variables
The “Checklist” - Risk drivers identification - Strategies
View in Lab:
Strategies
2 . Quest for invariance
The “Checklist” - Quest for invariance
View in Lab:
Quest for invariance
The “Checklist” - Quest for invariance - Efficiency: random walk
View in Lab:
Efficiency: random walk
Continuous-state random walk
Discrete-state random walk
Flexible combinations
The “Checklist” - Quest for invariance - Mean-reversion (continuous): ARMA
View in Lab:
Mean-reversion (continuous): ARMA
AR(1) process
AR(p) process
MA(q) process
ARMA(p,q) process
ARIMA(p,d,q) process
The “Checklist” - Quest for invariance - Mean-reversion (discrete): Markov chains
View in Lab:
Mean-reversion (discrete): Markov chains
Time-homogeneous Markov chains
Time-inhomogeneous Markov chains
Invariant and next-step function
Applications to credit risk
Connection with structural model
The “Checklist” - Quest for invariance - Long memory: fractional integration
View in Lab:
Long memory: fractional integration
The “Checklist” - Quest for invariance - Volatility clustering
View in Lab:
Volatility clustering
GARCH
Extensions of GARCH
Stochastic volatility
The “Checklist” - Quest for invariance - Multivariate quest
View in Lab:
Multivariate quest
Vector autoregression
Alternative models
The “Checklist” - Quest for invariance - Cointegration
View in Lab:
Cointegration
Modeling
Detection
Fit
The “Checklist” - Quest for invariance - Relationships among processes
View in Lab:
Relationships among processes
Inversion of first-degree lag polynomial
ARMA(p,q) processes as products of lag polynomials
Relationships between ARMA, MA and AR
AR(p) as VAR(1)
Univariate processes as VAR(1)
Relationships between VARMA, VMA and VAR
VAR(p) as VAR(1)
Multivariate processes as VAR(1)
Stationary as MA(∞): Wold representation
The “Checklist” - Quest for invariance - Toward machine learning
View in Lab:
Toward machine learning
Exogenous quest
Hidden quest
3 . Estimation
The “Checklist” - Estimation
View in Lab:
Estimation
The “Checklist” - Estimation - Setting the flexible probabilities
View in Lab:
Setting the flexible probabilities
Exponential decay and time conditioning
Kernels and state conditioning
Joint state and time conditioning
Statistical power of flexible probabilities
The “Checklist” - Estimation - Historical
View in Lab:
Historical
From historical distribution to flexible probabilities
Location-dispersion: HFP ellipsoid
Kernel estimation with flexible probabilities
The “Checklist” - Estimation - Maximum likelihood
View in Lab:
Maximum likelihood
From maximum likelihood to flexible probabilities
Exponential family invariants
Location-dispersion: normal MLFP ellipsoid
Location-dispersion: t MLFP ellipsoid
The “Checklist” - Estimation - Bayesian estimation
View in Lab:
Bayesian estimation
Exponential family invariants
Normal-inverse-Wishart prior distribution
Normal-inverse-Wishart posterior distribution
Student t predictive distribution
Shrinkage
Uncertainty
The “Checklist” - Estimation - Shrinkage
View in Lab:
Shrinkage
Mean shrinkage: James-Stein
Covariance shrinkage: Ledoit-Wolf
Correlation shrinkage: random matrix theory
Covariance shrinkage: sparse eigenvector rotations
Covariance shrinkage: glasso
The “Checklist” - Estimation - Generalized method of moments
View in Lab:
Generalized method of moments
Method of moments
Generalized method of moments - exact specification
Generalized method of moments - over specification
The “Checklist” - Estimation - Robustness
View in Lab:
Robustness
Local robustness
Global robustness
The “Checklist” - Estimation - Missing data
View in Lab:
Missing data
Randomly missing data
Times series of different length
Missing series
The “Checklist” - Estimation - (Dynamic) copula-marginal
View in Lab:
(Dynamic) copula-marginal
Static copula
Dynamic copula
The “Checklist” - Estimation - Estimation assessment
View in Lab:
Estimation assessment
Estimators as decisions
Frequentist approach
Bayesian approach
Analytical results
Monte Carlo simulations
Cross-validation
The “Checklist” - Estimation - Points of interest, pitfalls, practical tips
View in Lab:
Points of interest, pitfalls, practical tips
Unconditional estimation
Standardization
Non-synchronous data
High-frequency volatility/correlation
Outlier detection
Exponential moving moments and statistics
Backward/forward exponential decay
Combining estimation techniques
4 . Projection
The “Checklist” - Projection
View in Lab:
Projection
The “Checklist” - Projection - One-step historical projection
View in Lab:
One-step historical projection
The “Checklist” - Projection - Analytical
View in Lab:
Analytical
The “Checklist” - Projection - Monte Carlo
View in Lab:
Monte Carlo
Direct Monte Carlo
Copula-marginal
General-step Monte Carlo
The “Checklist” - Projection - Historical
View in Lab:
Historical
Historical bootstrapping
Hybrid Monte Carlo-historical
The “Checklist” - Projection - Application: multivariate Markov chains
View in Lab:
Application: multivariate Markov chains
Univariate Markov chain
Connection with structural credit model
Multivariate Markov chains
Connection with structural credit model
The “Checklist” - Projection - Square-root rule and generalizations
View in Lab:
Square-root rule and generalizations
Thin-tailed random walk
Thick-tailed random walk
Multivariate random walk
General processes
5 . Pricing at the horizon
The “Checklist” - Pricing at the horizon
View in Lab:
Pricing at the horizon
The “Checklist” - Pricing at the horizon - Exact repricing
View in Lab:
Exact repricing
Equities
Currencies
Fixed-income
Derivatives
Credit
High frequency
Strategies
The “Checklist” - Pricing at the horizon - Carry
View in Lab:
Carry
Equities
Currencies
Fixed-income
Derivatives
Other asset classes
The “Checklist” - Pricing at the horizon - Taylor approximations
View in Lab:
Taylor approximations
Equities
Fixed-income
Derivatives
Other asset classes
6 . Aggregation
The “Checklist” - Aggregation
View in Lab:
Aggregation
The “Checklist” - Portfolio aggregation - Basic toolkit aggregation
View in Lab:
Stock variables
Portfolio
Value
Exposure
Leverage
The “Checklist” - Portfolio aggregation - Static ex-ante performance
View in Lab:
Static market/credit risk
Standardized holdings and weights
Scenario-probability distribution
Elliptical distribution
Quadratic-normal distribution
The “Checklist” - Portfolio aggregation - Enterprise risk management
View in Lab:
Enterprise risk management
Portfolio: balance sheet
Performance: income statement
Operational risk
Banking
Insurance
The “Checklist” - Portfolio aggregation - Operational P&L/risk
The “Checklist” - Aggregation - Points of interest and pitfalls
View in Lab:
Points of interest and pitfalls
Solvency and collateral
Credit value adjustment
CreditRisk+ approximation
7 . Ex-ante evaluation
The “Checklist” - Ex-ante evaluation
View in Lab:
Ex-ante evaluation
The “Checklist” - Ex-ante evaluation - Stochastic dominance
View in Lab:
Stochastic dominance
The “Checklist” - Ex-ante evaluation - Satisfaction
View in Lab:
Satisfaction
The “Checklist” - Ex-ante evaluation - Mean-variance
View in Lab:
Mean-variance
Mean
Variance
Standard deviation
Mean-variance trade-off
A strange success story
The “Checklist” - Ex-ante evaluation - Expected utility and certainty-equivalent
View in Lab:
Expected utility and certainty-equivalent
Common utility functions
Computation and sensitivity analysis
The “Checklist” - Ex-ante evaluation - Quantile (value at risk)
View in Lab:
Quantile (value at risk)
Computation and sensitivity analysis
Cornish-Fisher approximation
Extreme value theory
The “Checklist” - Ex-ante evaluation - Coherent indices of satisfaction
View in Lab:
Coherent indices of satisfaction
Definition
Examples
Computation and sensitivity analysis
The “Checklist” - Ex-ante evaluation - Spectral indices of satisfaction
View in Lab:
Spectral indices of satisfaction
Definition
Computation and sensitivity analysis
Quantile (VaR) computations
cVaR computations
The “Checklist” - Ex-ante evaluation - Distortion measures
View in Lab:
Distortion measures
Definition
Equivalence between distortion and spectral indices
Examples
Computation and sensitivity analysis
The “Checklist” - Ex-ante evaluation - Non-dimensional ratios
View in Lab:
Non-dimensional ratios
Information ratio
Downside ratios
The “Checklist” - Ex-ante evaluation - Additional indices
View in Lab:
Additional indices
Alpha
Beta
Correlation
Buhlmann expectation
Esscher expectation
The “Checklist” - Ex-ante evaluation - Pitfalls, points of interest and practical tips
View in Lab:
Pitfalls, points of interest and practical tips
The Arrow-Pratt approximation of the certainty-equivalent
Utility versus spectrum functions
Spectral/distortion versus coherent measures
The Buhlmann and Esscher expectations are not distortion expectations
Indices of satisfaction under normality
Moments of the excess performance
8a . Ex-ante attribution: performance
The “Checklist” - Ex-ante attribution: performance
View in Lab:
Ex-ante attribution: performance
The “Checklist” - Ex-ante attribution: performance - Bottom-up exposures
View in Lab:
Bottom-up exposures
Pricing factors
Style factors/smart beta
The “Checklist” - Ex-ante attribution: performance - Top-down exposures: factors on demand
View in Lab:
Top-down exposures: factors on demand
The “Checklist” - Ex-ante attribution: performance - Joint distribution
View in Lab:
Joint distribution
Elliptical distribution
Scenario-probability distribution
The “Checklist” - Ex-ante attribution: performance - Applications
View in Lab:
Applications
Hedging
Portfolio-based risk-attribution
8b . Ex-ante attribution: risk
The “Checklist” - Ex-ante attribution: risk
View in Lab:
Ex-ante attribution: risk
The “Checklist” - Ex-ante attribution: risk - Risk attribution/risk budgeting: general criteria
View in Lab:
General criteria
Isolated/“first in”proportional attribution
“Last in”proportional attribution
Sequential attribution
Shapley attribution
The “Checklist” - Ex-ante attribution: risk - Homogenous measures and Euler decomposition
View in Lab:
Homogenous measures and Euler decomposition
Standard deviation
Variance
Certainty-equivalent
Distortion/spectral measures
Economic capital
The “Checklist” - Construction: portfolio optimization - A compromise: two-step mean-variance
View in Lab:
A compromise: two-step mean-variance
The “Checklist” - Construction: portfolio optimization - Analytical solutions of the mean-variance problem
View in Lab:
Analytical solutions of the mean-variance problem
9b . Construction: cross-sectional strategies
The “Checklist” - Construction: cross-sectional strategies
View in Lab:
Construction: cross-sectional strategies
The “Checklist” - Construction: cross-sectional strategies - Simplistic portfolio construction
View in Lab:
Simplistic portfolio construction
The “Checklist” - Construction: cross-sectional strategies - Signal characteristic
View in Lab:
Advanced portfolio construction
Characteristic portfolio
Signal-induced factor
Flexible factor
The “Checklist” - Construction: cross-sectional strategies - Factor portfolios
View in Lab:
Relationship with FLAM and APT
Signal-induced moments of the P&L
Fundamental law of active management
APT assumption
The “Checklist” - Construction: cross-sectional strategies - Multiple signals
View in Lab:
Multiple portfolios
Characteristic portfolios
Signal-induced factors
Flexible factors
Relationship with FLAM and APT
The “Checklist” - Construction: cross-sectional strategies - Backtesting
View in Lab:
Backtesting
The “Checklist” - Construction: cross-sectional strategies - Points of interest, pitfalls, practical tips
View in Lab:
Points of interest, pitfalls, practical tips
Machine learning
Generalized fundamental law of active management
9c . Construction: time series strategies
The “Checklist” - Construction: time series strategies
View in Lab:
Construction: time series strategies
The “Checklist” - Construction: time series strategies - The market
View in Lab:
The market
Risky investment
Low-risk investment
Strategies
The “Checklist” - Construction: time series strategies - Expected utility maximization
View in Lab:
Expected utility maximization
The objective
Optimization
The “Checklist” - Construction: time series strategies - Option-based portfolio insurance
View in Lab:
Option based portfolio insurance
Payoff design
Partial differential equation
Budget
Policy
A unified approach
The “Checklist” - Construction: time series strategies - Rolling horizon heuristics
View in Lab:
Rolling horizon heuristics
Constant proportion portfolio insurance
Drawdown control
Signal induced strategy
10 . Execution
The “Checklist” - Execution
View in Lab:
Execution
The “Checklist” - Execution - Market impact modeling
View in Lab:
Market impact modeling
Liquidity curve
Exogenous impact
Endogenous impact
The “Checklist” - Execution - Order scheduling
View in Lab:
Order scheduling
Trading P&L decomposition
Model P&L
Moments of model P&L
Model P&L optimization
Quasi-optimal P&L distribution
The “Checklist” - Execution - Order placement
View in Lab:
Order placement
Step 1: order scheduling
Step 2: order placement
11 . Executive summary
Factor models and learning - Executive summary
Factor models and learning - Non-parametric linear factor models - Theory
View in Lab:
Theory
Dominant-residual models
Systematic-idiosyncratic models
Factor models and learning - Non-parametric linear factor models - Estimation
View in Lab:
Estimation
Time series models
Data fit
Factor models and learning - Non-parametric regression LFM - Theory
View in Lab:
Theory
Solution: factor loadings
Recovery and fit
Residuals features
Natural scatter specification
Factor models and learning - Non-parametric regression LFM - Estimation
View in Lab:
Estimation
Factor models and learning - Non-parametric principal-component LFM - Theory
View in Lab:
Theory
Principal component analysis
Statistics
Algebra
Geometry
Solution: factor loadings and factor-construction matrix
Recovery and fit
Residuals features
Natural scatter specification
Factor models and learning - Non-parametric principal-component LFM - Estimation
View in Lab:
Estimation
Factor models and learning - Non-parametric principal-component LFM - Case study: swap market
View in Lab:
Case study: swap market
Finite set of times to maturity
The continuum limit
Factor models and learning - Non-parametric systematic-idiosyncratic LFM - Theory
View in Lab:
Theory
Implications on parameters
Implications on covariance
Loadings unearthing
Approximate factor extraction
Factor models and learning - Non-parametric systematic-idiosyncratic LFM - Estimation
View in Lab:
Estimation
Factor models and learning - Non-parametric cross-sectional LFM - Theory
View in Lab:
Theory
Solution: factor-construction matrix
Recovery and fit
Residuals features
Natural scatter specification
Systematic-idiosycratic assumption
Factor models and learning - Non-parametric cross-sectional LFM - Estimation
View in Lab:
Estimation
Factor construction
Problems with pure cross-sectional estimation
Hybrid cross-sectional estimation
Factor models and learning - Non-parametric LFM's: points of interest - Truncation
View in Lab:
Truncation
Factor models and learning - Dynamic models - Dynamic regression
View in Lab:
Wiener-Kolmogorov filtering
The solution in population
The solution in sample
Factor models and learning - Dynamic models - Dynamic principal component
View in Lab:
Dynamic principal component
The solution in population
Computational issue
The solution in sample
Factor models and learning - Dynamic models - State space model
View in Lab:
Linear state space models
Model
Static case
Dynamic case
Factor models and learning - Application: regression - Maximum likelihood
View in Lab:
Maximum likelihood
Iteration toward the maximum
Factor models and learning - Application: regression - Regularization
View in Lab:
Regularization
Step-wise regression selection
Lasso regression
Ridge regression
Covariance shrinkage
Factor models and learning - Application: regression - Bayesian
View in Lab:
Bayesian
Normal conditional likelihood
Normal-inverse-Wishart prior distribution
Normal-inverse-Wishart posterior distribution
Student t predictive distribution
Shrinkage
Uncertainty
Valuation - Valuation foundations - Foundations
View in Lab:
Valuation foundations
Instruments
Value
Cash-flows
Re-invested cash-flows
Cash-flow adjusted value
Profit-and-loss (P&L)
Payoff
Valuation - Background definitions - Points of interest and pitfalls
View in Lab:
Points of interest and pitfalls
Value versus price
Multi-currency conversions
Actual versus simple P&L
Valuation - Linear pricing theory: core - Fundamental axioms
View in Lab:
Fundamental axioms
Law of one price
Linearity
No arbitrage
Valuation - Linear pricing theory: core - Stochastic discount factor
View in Lab:
Stochastic discount factor
Identification
Misidentification
Valuation - Linear pricing theory: core - Fundamental theorem of asset pricing
View in Lab:
Fundamental theorem of asset pricing
Valuation - Linear pricing theory: core - Risk-neutral pricing
View in Lab:
Risk-neutral pricing
General case
No rebalancing limit: forward measure
Continuous rebalancing limit
Valuation - Linear pricing theory: core - Capital asset pricing model framework
View in Lab:
Capital asset pricing model framework
Maximum Sharpe ratio portfolio
Security market line
Alternative derivation: linear factor model for stochastic discount factor
Valuation - Linear pricing theory: core - Covariance principle
View in Lab:
Covariance principle
Valuation - Linear pricing theory: further assumptions - Completeness
View in Lab:
Completeness
Definition
Pricing
Arrow-Debreu securities
Stochastic discount factor
Valuation - Linear pricing theory: further assumptions - Equilibrium: pure capital asset pricing model
View in Lab:
Equilibrium: pure capital asset pricing model
Valuation - Linear pricing theory: further assumptions - Arbitrage pricing theory
View in Lab:
Arbitrage pricing theory
Standard derivation: linear factor model for instruments
Alternative derivation: linear factor model for stochastic discount factor
Valuation - Linear pricing theory: further assumptions - Intertemporal consistency
View in Lab:
Intertemporal consistency
Continuous time variables
Martingales
Heuristic for stochastic discount factor time consistency
Heuristic for numeraire martingale
Valuation - Non-linear pricing theory - Fundamental axioms
View in Lab:
Fundamental axioms
Law of one price
Non-linearity
Arbitrage
Valuation - Non-linear pricing theory - Valuation as evaluation
View in Lab:
Valuation as evaluation
Variance and other shift principles
Certainty-equivalent principle
Distortion principles
Esscher principle
Valuation - Valuation implementation - Fixed income
View in Lab:
Fixed-income
Vasicek
Other models
Valuation recipe
Performance analysis - Performance definitions - Holding P&L of a portfolio
View in Lab:
Holding P&L of a portfolio
Performance analysis - Performance definitions - Returns
View in Lab:
Returns
Basic definitions
Standard linear returns and weights
Generalized linear returns
Generalized weights and aggregation
Investments with capital injection
Log-returns
Performance analysis - Performance definitions - Excess performance
View in Lab:
Excess performance
Benchmark
Excess return
Quant toolbox - Multivariate distributions - Representations of a distribution
View in Lab:
Representations of a distribution
Quant toolbox - Multivariate distributions - Marginalization
View in Lab:
Marginalization
Quant toolbox - Multivariate distributions - Elliptical distributions
View in Lab:
Elliptical distributions
Fundamental concepts
Stochastic representations
Moments and dependence
Affine equivariance
Notable elliptical distributions
Generation of elliptical scenarios
Scenario generation with dimension reduction
Quant toolbox - Multivariate distributions - Scenario-probability distributions
View in Lab:
Scenario-probability distributions
Types of scenario-probability distributions
Probability density function
Transformations and generalized expectations
Cumulative distribution function
Quantile
Smooth quantile
Moments and other statistical features
Quant toolbox - Multivariate distributions - Exponential family distributions
View in Lab:
Exponential family distributions
Normal distribution
Scenario-probability distribution
Quant toolbox - Multivariate distributions - Other special classes of distributions
View in Lab:
Other special classes of distributions
Stable distributions
Infinitely divisible distributions
Quant toolbox - Multivariate distributions - Notable specific distributions
View in Lab:
Notable specific distributions
Uniform distribution
Quadratic-normal distribution
Wishart distribution
Quant toolbox - Estimation techiniques - Maximum likelihood
View in Lab:
Maximum likelihood
General formulation
Hidden variables
Relevant cases
Numerical methods
Quant toolbox - Estimation techiniques - Bayesian statistics
View in Lab:
Bayesian statistics
Conditional likelihood, prior, posterior, predictive
Classical-equivalent and estimation uncertainty
Shrinkage
Analytical results
Numerical methods
37 . Views processing
Quant toolbox - Views processing
View in Lab:
Views processing
Quant toolbox - Views processing - Theory
View in Lab:
Theory: minimum relative entropy
Prior and view variables
Point views
Distributional views
Partial views
Partial views on generalized expectations
Sanity check
Confidence
Quant toolbox - Views processing - Partial views: analytical implementation
View in Lab:
Partial views: analytical implementation
Prior distribution
Views
Sanity check
Posterior distribution
Views intensity
Confidence
Relevant special cases
Quant toolbox - Black-Litterman - Equilibrium prior distribution
View in Lab:
Equilibrium prior distribution
Quant toolbox - Black-Litterman - Views
View in Lab:
Views
Quant toolbox - Black-litterman - Sanity check
View in Lab:
Sanity check
Quant toolbox - Black-Litterman - Posterior distribution
View in Lab:
Posterior distribution
Quant toolbox - Black-Litterman - Limit cases
View in Lab:
Limit cases
High confidence in prior
Low confidence in views
Full confidence in views
Quant toolbox - Black-Litterman - Generalizations
View in Lab:
Generalizations
From linear returns to risk drivers
From stock-like to generic asset classes
From normal to non-normal markets
From linear equality views to partial flexible views
Quant toolbox - Geometry of random variables - The r-squared
View in Lab:
The r-squared
Definition
Relation to distance
Quant toolbox - Information geometry primer - Distributions geometry
View in Lab:
Distributions geometry
Fisher metric: length and volume
Flatness and geodesics
Duality: potentials and Legendre transformations
Distance and divergence
41 . Decision theory with model uncertainty
Quant toolbox - Decision theory with model uncertainty
View in Lab:
Decision theory with model uncertainty
Quant toolbox - Decision theory with model uncertainty - Foundations of decision theory
View in Lab:
Foundations of decision theory
Fundamental concepts
Frequentist approach
Bayesian approach
Model risk, estimation risk
Quant toolbox - Copulas - Univariate results
View in Lab:
Univariate results
Quant toolbox - Copulas - Definition and properties of copulas
View in Lab:
Definition and properties of copulas
Grades
Copula
Sklar’s theorem
Copula invariance
Quant toolbox - Copulas - Special classes of copulas
View in Lab:
Special classes of copulas
Elliptical copulas
Archimedean copulas
Quant toolbox - Copulas - Copula-marginal separation
View in Lab:
Copula-marginal separation
Quant toolbox - Copulas - Copula-marginal combination
View in Lab:
Copula-marginal combination
Quant toolbox - Location and dispersion - Univariate location-dispersion
View in Lab:
Univariate location-dispersion
Z-score and affine equivariance
Taxonomy of location-dispersion features
Quant toolbox - Location and dispersion - Multivariate location-dispersion
View in Lab:
Multivariate location-dispersion
Tentative visualizations in low dimension
Location-dispersion ellipsoid
Affine equivariance
Taxonomy of multivariate location-dispersion features
Quant toolbox - Location and dispersion - Expectation and covariance
View in Lab:
Expectation and covariance
Definitions
Generalized affine equivariance
Connections with calculus
Connections with probability
45 . Invariance tests
Quant toolbox - Invariance tests
View in Lab:
Invariance tests
Quant toolbox - Invariance tests - Simple tests
View in Lab:
Simple tests
Quant toolbox - Continuous time processes - Efficiency: Lévy processes
View in Lab:
Efficiency: Lévy processes
Infinite divisibility
Continuous state: Brownian diffusion
Discrete state: Poisson jumps
Lévy-Khintchine representation
Subordination
Quant toolbox - Continuous time processes - Mean-reversion (continuous)
View in Lab:
Mean-reversion (continuous)
Ornstein-Uhlenbeck process
Square-root process and other generalizations
Quant toolbox - Continuous time processes - Mean-reversion (discrete): Markov chain generator
View in Lab:
Mean-reversion (discrete): Markov chain generator
Time-homogeneous generator
Time-inhomogeneous generator
Quant toolbox - Continuous time processes - Long memory: fractional Brownian motion
View in Lab:
Long memory: fractional Brownian motion
Fractional Brownian motion
Quant toolbox - Continuous time processes - Volatility clustering
View in Lab:
Volatility clustering
Stochastic volatility
Time change
Connection between time-changed Brownian motion and stochastic volatility
Quant toolbox - VAR(1)/Multivariate Ornstein-Uhlenbeck - AR(1)
View in Lab:
AR(1)
Conditional distribution of AR(1)
Stationarity and unconditional distribution of AR(1)
Quant toolbox - VAR(1)/Multivariate Ornstein-Uhlenbeck - VAR(1)
View in Lab:
VAR(1)
Conditional distribution of VAR(1)
Stationarity and unconditional distribution of VAR(1)
Cointegrated VAR(1)
Quant toolbox - VAR(1)/Multivariate Ornstein-Uhlenbeck - Ornstein-Uhlenbeck
View in Lab:
Ornstein-Uhlenbeck
Conditional distribution of OU
Stationarity and unconditional distribution of OU
Quant toolbox - VAR(1)/Multivariate Ornstein-Uhlenbeck - Multivariate Ornstein-Uhlenbeck
View in Lab:
Multivariate Ornstein-Uhlenbeck
Conditional distribution of MVOU
Stationarity and unconditional distribution of MVOU
Geometrical interpretation∗
Cointegrated Ornstein-Uhlenbeck
Quant toolbox - VAR(1)/Multivariate Ornstein-Uhlenbeck - Rel. between (V)AR and (MV)OU
View in Lab:
Relationship between (V)AR and (MV)OU
MVOU is VAR(1)
VAR(1) is MVOU
Quant toolbox - Signals - Value signals
View in Lab:
Value signals
Book
Pricing
Quant toolbox - Signals - Technical signals
View in Lab:
Technical signals
Momentum
Filters
Cointegration
Quant toolbox - Signals - Microstructure signals
View in Lab:
Microstructure signals
Trade autocorrelation
Order imbalance
Price prediction
Volume clustering
Quant toolbox - Signals - Fundamental and other signals
View in Lab:
Fundamental and other signals
Quant toolbox - Signals - Signal processing
View in Lab:
Signal processing
Smoothing
Scoring
Ranking
Quant toolbox - Optimization primer - Convex programming
View in Lab:
Convex programming
Conic programming
Second-order cone programming
Quadratic programming
Linear programming
Semidefinite programming
Quant toolbox - Optimization primer - Integer n-choose-k selection
View in Lab:
Integer ¯n-choose-k selection
Naive selection
Forward step-wise selection
Backward step-wise selection
Lasso
Quant toolbox - Useful algorithms - Factor analysis algorithms
View in Lab:
Factor analysis algorithms
Principal axis factorization
Maximum likelihood factorization
Pay attention, please:
This website needs Javascript support enabled to work. Without this, the most of functions will be disabled.