Functional Principal Component Analysis for Derivatives of High-Dimensional Curves
Maria Grith, Humboldt-Universität zu Berlin, Germany
Date:
16 Apr 2014
Time:
3.00pm – 4.00pm
Venue:
S16-06-118 DSAP seminar room
(This seminar is organized jointly with the Department of Statistics and Applied Probability (DSAP))
About the Speaker
Maria Grith is currently visiting the Quantitative Finance group as a postdoctoral scholar at the Lee Kong Chian School of Business, at the Singapore Management University. Maria completed her Doctorate in Economics and Master of Science at the Humboldt-Universität zu Berlin, and her undergraduate studies at the West University of Timisoara. At the Humboldt-Universität zu Berlin, she is the primary instructor for lectures on Statistics of Financial Markets, Multivariate Statistical Analysis, Non and Semi-parametric Modeling, and Numerical Introductory Course.
Abstract
This study is motivated by the evolution of state price densities (SPD) implied by option data. For a fixed maturity and under some general arbitrage conditions the SPD is proportional to the quotient of the European call options with respect to the strike price. If only options with a pre-specified maturity are to be analyzed, then SPDs are one-dimensional functions. A two-dimensional point of view can be adopted if maturities are taken as an additional argument and the SPDs are viewed as a family of curves. Our paper addresses both the challenge of statistical modeling the derivatives of higher dimensional functions and that of extracting the economic content embedded in the dynamics of SPD functions. We analyze a sample of noisy curves, recover their derivatives using functional principal component analysis and summarize their time variability with a few interpretable parameters. This is a joint work with Wolfgang K. Hardle, Alois Kneip and Heiko Wagner.
