Regression & Time Series
Regression: linear/nonlinear, parametric/nonparametric. Measure influence and
robustness. Kernel, projection pursuit and neural networks.
Midterm project: nonparametric option pricing.
Time series: AR, MA, ARMA, ARIMA, models, linear systems and Kalman filter.
ARCH and GARCH models as motivated by financial applications.
Final Project: prediction of 4 sub-indices of the S&P 500.
Homework + Midterm + Final require the use of Splus.
Stochastic Calculus & Financial
Binomial trees, random walk and discrete time martingales. Wiener process,
stochastic integration, Ito processes, semimartingales and stochastic
differential equations. Stochastic market models and arbitrage
pricing. Exotic and interest rate derivatives. Incomplete models. Pricing
risky bonds and weather derivatives.
ORF 557: Seminar on Extreme Value Theory
VaR as a motivation. Classical limit theorems for sums and maxima.
Extreme value distributions and their statistical estimation.
Analysis of insurance and financial case studies.