Statistical Methods for Quantitative Finance

This course reviews basic statistical methods needed in quantitative and computational finance. Upon completion of this course, students will have mastered the necessary probability and statistics tools for study of quantitative finance areas such as options and derivatives, portfolio optimization, fixed income, and quantitative risk management

The main areas of focus are: probability theory; random variables and their distributions; transformation of random variables; limit theorems; and parameter estimation theory. Topics include:

• Probability theory: set theory, probability spaces, joint probability, conditional probability, Bayes theorem
• Univariate and multivariate random variables: distribution and density functions, moments, transformations, conditional expectations
• Limit theorems: random variable convergence types, law of large numbers, central limit theorems
• Parameter estimation theory: variance, bias and mean-squared error, minimum variance unbiased estimation (MVUE), maximum likelihood estimation

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