STATISTICAL ANALYSIS OF FINANCIAL DATA

Code: MA373 | L-T-P-C: 3-0-2-8

Prerequisites: MA371

Introduction to S-Plus and data analysis: Financial data, random variables and their distributions, exploratory data analysis tools, kernel density estimation; Quantiles and Q-Q plots; Random generators and Monte Carlo samples; Continuous time processes: Maximum likelihood estimation (MLE) for common diffusion processes (Brownian Motion, Ornstein-Uhlenbeck, Cox-Ingersoll-Ross), approximate MLE of general diffusions, simulation of exact method for common diffusions, Euler and Milstein discretization schemes for general diffusions. Time series analysis: AR, MA, ARMA, ARCH and GARCH models; Identification, estimation and forecasting; Stochastic volatility time series models for term structure of interest rates. Multivariate Data Analysis: Multivariate normal samples, estimation, hypothesis testing, and simulation; Copulas and random simulations, examples of copulas families, fitting Copulas, Monte Carlo simulations with Copulas; Dimension reduction techniques, Principal Component Analysis. Elements of extreme value theory: Generalized extreme value (GEV) and generalized Pareto distribution (GPD); Block maxima, GPD and Hill methods; Quantile estimation with the Cornish-Fisher expansion.

Texts:

1. R. A. Carmona, Statistical Analysis of Financial Data in S-PLUS, Springer, 2004.
2. E. Zivot and J. Wang, Modeling Financial Time Series with S-PLUS, 2nd Edition, Springer, 2006.
3. P. Glasserman, Monte Carlo Methods in Financial Engineering, Springer, 2004.