UCLA

The availability of software tools, high frequency data, and

recent advances in statistical inference all allow a greater study of

continuous-time models of price and volatility processes.

This research studies the structure of intraday stock volatility over

a selected group of stocks from 2007 to 2011. We use nearly every

valid transaction in the Trades and Quotes database to obtain a price

series which is sampled every second. We calculate realized variation

(RV), the sum of squared log returns, to estimate squared volatility.

We partition the trading day at the level of 100-second time

intervals, and we observe mean reversion in RV even at this time

scale. We estimate a modified Heston model for RV in which

statistical criteria are used to detect volatility jumps.