02 Quantitative Analysis

QTA 1: Fundamentals of Probability

What a sample space, an event, and an event space are Statistics, econometrics and risk management all sit on top of probability. Many events a risk manager cares about carry a number, such as the los

QTA 2: Random Variables

What a random variable is and how a realization differs from the variable Probability is built on events, and an event is an abstract object: the coin landing heads, the borrower failing to pay. Abstr

QTA 3: Common Univariate Random Variables

Which probability distributions risk managers use, and how PMF, PDF and CDF differ Statisticians have named well over two hundred distributions. A risk manager needs about eleven. Each survivor matche

QTA 4: Multivariate Random Variables

What a bivariate random variable is and how its joint PMF works A multivariate random variable is a vector of random variables, an ordered collection whose members are called components. Give it two a

QTA 5: Sample Moments

Population moments and sample moments: estimator versus estimate A random variable carries fixed numerical features: a mean, a variance, a skewness, a kurtosis. These are population moments, belonging

QTA 6: Hypothesis Testing

What a hypothesis test is and the six elements it contains The true values of population parameters sit out of reach, since nobody observes an entire population. A sample is what is available, and it

QTA 7: Linear Regression

What linear regression is and the bivariate regression model Two random variables move together, and the question is how much of one moves with the other. Regression is the workhorse answer, the most

QTA 8: Regression with Multiple Explanatory Variables

What the multiple regression model is and how it extends simple regression A regression built on a single explanatory variable teaches the mechanics of ordinary least squares cleanly, but it rarely ma

QTA 9: Regression Diagnostics

Omitted variable bias: what happens when a relevant regressor is left out A regression is only as trustworthy as the list of variables it carries. The ideal specification holds everything that moves t

QTA 10: Stationary Time Series

What a stochastic process is and how a time series decomposes Interest rates, credit spreads and growth rates carry pieces of their own past, and that memory is what makes forecasting worth attempting

QTA 11: Non-Stationary Time Series

What makes a time series non-stationary: trends, seasonality and unit roots A covariance-stationary series holds its mean, its variance and its autocovariances steady wherever in the sample you look,

QTA 12: Measuring Returns, Volatility, and Correlation

Simple returns and continuously compounded returns: formulas and conversion Every volatility estimate starts from a series of returns, so the definition picked at the outset shapes what follows. Buy a

QTA 13: Simulation and Bootstrapping

What Monte Carlo simulation is and how it differs from bootstrapping Risk managers reach for simulation whenever the quantity they want cannot be written down in closed form. Three familiar uses give

QTA 14: Machine-Learning Methods

How machine learning differs from classical econometrics Machine learning is a broad label rather than a single method. It covers any procedure in which a model is trained on data until it picks out p

QTA 15: Machine Learning and Prediction

How to encode categorical variables: dummy variables and one-hot encoding Much of what a risk model wants to use arrives as words: a borrower lives in one region, a company sits in the technology sect