Prerequisites: One year of Calculus. Probability spaces, distributions (with an emphasis on distributions that are important for financial applications, e.g. lognormal and heavy-tailed distributions), random variables, VaR, multivariate distributions (including multivariate normal), copulas, expectation, conditional probability and expectation, binomial options pricing model, law of large numbers, central limit theorem.
Theory of point and interval estimation and their relevance for estimating returns, volatility, and correlation. Topics covered include method of moments, maximum likelihood, unbiasedness, mean-squared error, sufficiency, and Cramer-Rao lower bound. Hypothesis testing. Factor models and principal components analysis in finance. Introduction to nonparametric regression.