Quant Marathon: Data Science for Finance Module Program

Dependence - correlation and copula

• Key notation tenets

• Jointness: correlation

• Jointness: copula

• Grades and inverse sampling

• Definition of copula

• Properties of copula and dependence structures

• Elliptical copulas

• Copulas implementation

Stochastic processes

• Main definitions

• Stationarity

• Prediction

• Random walk

• Lévy processes

• Square-root rule and generalizations

Autoregressive processes

• Introduction

• Autoregression of order one

• Vector autoregression of order one

• Ornstein-Uhlenbeck process

• Multivariate Ornstein-Uhlenbeck

• Linear state-space models

Covariance stationary theory

• Introduction

• Spectral analysis

• Filtering

• Wold decomposition

• Dynamic factor models

• Wiener-Kolmogorov filter

Probabilistic models

• Markov processes

• Markov chains

• State-space processes

• GARCH

• Stochastic volatility

• Probabilistic forecasting

• Markov processes forecasting

• State-space processes forecasting

Generalized inference

• Black litterman: equilibrium prior

• Black litterman: active views

• Black litterman: limit cases and generalizations

• Partial views and minimum relative entropy

• Partial views: analytical implementation

• Partial views: flexible probabilities implementation

Course 3: Data Science for Finance