AMS 516: Statistical Methods in Finance

The course introduces statistical methodologies in quantitative finance. Financial applications and statistical methodologies are intertwined in all lectures. The course will cover regression analysis and applications to the Capital Asset Pricing Model and multifactor pricing models, principal components and multivariate analysis, statistical methods for financial time series; value at risk, smoothing techniques and estimation of yield curves, and estimation and modeling of volatilities.

Required Textbook: Statistical Models and Methods for Financial Markets by Tze Leung Lai and Haipeng Xing, 2008, Springer

Learning Outcomes

1. Build statistical models of phenomena in finance, in particular:
   • Markowtiz portfolio optimization;
   • Multi-factor pricing;
   • Investment theory;
   • Time-varying volatilities;
   • Market risk.
2. Demonstrate skill with solution methods for implementing Markowtiz portfolio optimization
   • Likelihood inference;
   • Bayesian methods;
   • Shrinkage and regularization;
   • Resampled efficient frontier;
   • Multivariate analysis (principle component analysis and factor analysis);
   • Bayesian nonparametric control.
3. Demonstrate skill with the theory for portfolio optimization.
   • Markowitz’s mean-variance efficient frontier;
   • Risk-measured based portfolio management;
   • Multi-factor asset pricing models.
4. Use computer software techniques to validate analytical solutions, and to visualize solutions of portfolio optimization.