**Date & Time:** Monday, January 18, 2010 15:30-16:30.

**Venue:** Ramanujan Hall

**Title:** Functional Data Analysis for Volatility

**Speaker:** Rituparna Sen, UC Davis, University of California

**Abstract:** We introduce a functional volatility process that provides a novel tool
for modeling volatility trajectories in financial markets. Volatility of
returns is assumed to result from a smooth functional volatility process
in combination with a multiplicative white noise. In our model, random
trajectories of volatility are a hidden component of financial markets for
which only implicit and indirect information is available through observed
returns. Functional principal component analysis that relies on the
Karhunen-Love decomposition based on data that reflect repeated patterns
allows to empirically characterize the underlying functional volatility
process. We describe the implementation of the corresponding functional
methods, provide asymptotic justifications, and illustrate the approach
with an analysis of volatility patterns inherent in intra-day trading of
various stocks. We also propose and evaluate the prediction of volatility
by applying functional regression techniques based on functional principal
component scores of the functional volatility process. This approach can
be used to detect days on which the stock price process has jumps and to
measure the size of jumps. Thus we can separate the jump component from
the integrated volatility in the quadratic variation process. This
separation leads to better prediction of integrated volatility. This
result is particularly useful for high-frequency data, because existing
measures like realized variation and bipower variation require sampling at
long horizons to get rid of microstructure noise. We develop the theory
and present examples with real data on indices and exchange rates.