AMS 522, Bayesian Methods in Finance

The course explores in depth the fundamentals of the Bayesian methodology and the use of the Bayesian theory in portfolio and risk management. It focuses on, among other topics incorporating the prior views of analysts and investors into the asset allocation process, estimating and predicting volatility, improving risk forecasts, and combining the conclusions of different models. Numerical exercises and projects in a high-level programming environment will be assigned.

Prerequisite: AMS 512 or instructor consent

Spring, 3 credits, ABCF grading

 

Textbooks for Spring 2023 Semester:

Required:  "Bayesian Methods in Finance" by S. Rachev, J. Hsu, B. Bagasheva, and F. Fabozzi, Wiley 2008; ISBN: 978-0-471-92083-0

Recommended:  "Risk and Asset Allocation" by Attilio Meucci; 1st ed. 2005. Corrr. 3rd printing 2009 edition, Springer Finance: ISBN: 978-3642009648 (soft cover)

Course notes will be provided for several modules which are not covered in the books.

 

Learning Outcomes:

1) Understand the framework of Bayesian setting and its difference with classical statistics
      * Prior and posterior distribution and information;
      * Bayesian theorem: discrete and continuous version;
      * Maximum likelihood methods.

2) Demonstrate skill with mathematical and statistical methods of Bayesian Paradig
      * Posterior inference;
      * Bayesian Predictive Inference;
      * Commonly used statistical distributions: Multivariate normal/t, inverted chi square, etc.

3) Understand the concepts and methods in Bayesian linear regression model and multi-factor model
      * Univariate linear regression using prior information;
      * Multivariate linear regression using prior information;
      * Multifactor model.

4) Demonstrate skill with numerical methods of computation.
      * Algorithms for posterior simulation;
      * Monte Carlo integration;
      * Logistic regression.

5) Understand the methodology of Bayesian framework of portfolio allocation.
      * Classical and Bayesian portfolio selection;
      * Shrinkage estimator;
      * Black-Litterman portfolio selection framework.

6) Understand the methods in Bayesian framework of volatility models.
      * GARCH type model;
      * Stochastic Volatility model.