The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

In this article we provide an asymptotic distribution theory for some nonparametric tests of
the hypothesis that asset prices have continuous sample paths. We study the behaviour of …

This paper shows how to use realized kernels to carry out efficient feasible inference on the
ex post variation of underlying equity prices in the presence of simple models of market …

In theory, the sum of squares of log returns sampled at high frequency estimates their
variance. When market microstructure noise is present but unaccounted for, however, we …

Stochastic di? erential equations model stochastic evolution as time evolves. These models
have a variety of applications in many disciplines and emerge naturally in the study of many …

A recent and extensive literature has pioneered the summing of squared observed intra-
daily returns,“realized variance”, to estimate the daily integrated variance of financial asset …

With the availability of high-frequency financial data, nonparametric estimation of the
volatility of an asset return process becomes feasible. A major problem is how to estimate …

We introduce a new stochastic model for the variations of asset prices at the tick-by-tick level
in dimension 1 (for a single asset) and 2 (for a pair of assets). The construction is based on …

We analyze the impact of time series dependence in market microstructure noise on the
properties of estimators of the integrated volatility of an asset price based on data sampled …

We show how pre-averaging can be applied to the problem of measuring the ex-post
covariance of financial asset returns under microstructure noise and non-synchronous …