A nonparametric estimator is proposed for the class of integrated cross volatilities of the form∫

1

0

f(

X

t

)σ

2

t

dt

where

f

is a continuous function

σ

2

s

is the instantaneous cross volatility of continuous semimartingale

X.

Using “Realized Volatility”

the asymptotic properties

which include consistency and asymptotic normality are obtained. A studentized version has been given and this can be used to construct confidence interval and do hypothesis testing.