MF 593 - Statistical Analysis of Financial Data

Fall 2007

Lectures: SMG 220
Tue, Thu 11-12.30
Instructor:
Paolo Guasoni
Office:
143 Bay State Rd, 4th floor
Phone:
(617) 353-4992
e-mail:
WWW:
http://math.bu.edu/people/guasoni
Office hours:
Tue, Thu 2:30-4:00, or by appointment
Teaching Fellow:
Gu Wang, guwang@bu.edu
Textbooks:
Required:
Statistical Analysis of Financial Data in S-PLUS
by Rene A. Carmona
Springer
ISBN: 0387202862
 Recommended:
An Introduction to R
by W. N. Venables, D. M. Smith
and the R Development Core Team
Objectives and Prerequisites:
This course covers an array of statistical techniques used for simulation, parameter estimation and forecasting in Finance. Prerequisites are knowledge of Probability and Calculus for one or more variables.
Course Outline:
  1. Introduction to R and Exploratory Data Analysis:
    1. Stylized features of financial data.
    2. Kernel density estimation. Q-Q plots.
    3. Random generators and Monte Carlo samples.
  2. Continuous time processes:
    1. Maximum likelihood estimation for common diffusion processes: Brownian Motion, Ornstein-Uhlenbeck, Cox-Ingersoll-Ross.
    2. Approximate MLE of general diffusions.
    3. Simulation: exact method for common diffusions.
    4. Euler and Milstein discretization schemes for general diffusions.
  3. Time series analysis:
    1. Linear models: AR, MA, ARMA. Identification, estimation and forecasting.
    2. Nonlinear models: ARCH and GARCH. Identification, estimation and forecasting.
  4. Multivariate Data Analysis:
    1. Multivariate normal samples: estimation, hypothesis testing, and simulation.
    2. Dependence and copulas: examples of copulas families, fitting and simulation.
    3. Dimension reduction techniques. Principal Component Analysis.
  5. Elements of Extreme Value Theory:
    1. Generalized Extreme Value (GEV) and Generalized Pareto Distribution (GPD).
    2. Block maxima, GPD and Hill methods.
    3. Quantile estimation with the Cornish-Fisher expansion.
Exam:
There will be homework assignments and a project.
Grades will be assigned as follows:
  • Homework: 60 %
  • Project: 40%
Rules: No late homework will be accepted.
Exams are open books and notebooks.
Calculators of any kind may be used freely.
Instances of cheating will be dealt with in accordance with University policy, and may result in failure of the course.