The
Department of Mathematical
Sciences
Financial Mathematics Seminar
presents
Dr. Yan Yu
Associate Professor
Department of
Quantitative Analysis and Operations Management
http://statqa.cba.uc.edu/~yuy/index.htm
Wednesday, April 16, 2008
4:30 - 5:30 pm
Room 325 Braunstein Hall
SEMIPARAMETRIC ESTIMATION For
TIME-INHOMOGENEOUS DIFFUSION PROCESSES
Abstract:
We develop two likelihood based approaches to semiparametrically
estimate a class of time-inhomogeneous diffusion process: log penalized splines (P-splines) and the local
log-linear method. Positive volatility is naturally embedded and this positivity is not guaranteed in most existing diffusion
models. We investigate different smoothing parameter selection. Separate
bandwidths are used for drift and volatility estimation. In the log P-splines approach, different smoothness for different time
varying coefficients is feasible by assigning different penalty parameters. We
also provide accompanying theorems for both approaches and report statistical
inference results. Finally, we present a case study using the weekly
three-month Treasury bill data from 1954 to 2004. We find that the log P-splines approach seems to capture the volatility dip in
mid-1960s the best. We also present an application of calculating a financial
market risk measure called Value at Risk (VaR) using
statistical estimates from log P-splines.