  Realized statistics based on high frequency returns have become very popular
in financial economics. In recent years, different non-parametric estimators of
the variation of a log-price process have appeared. These were developed by
many authors and were motivated by the existence of complete records of price
data. Among them are the realized quadratic (co-)variation which is perhaps the
most well known example, providing a consistent estimator of the integrated
(co-)volatility when the logarithmic price process is continuous. Limit results
such as the weak law of large numbers or the central limit theorem have been
proved in different contexts. In this paper, we propose to study the large
deviation properties of realized (co-)volatility (i.e., when the number of high
frequency observations in a fixed time interval increases to infinity. More
specifically, we consider a bivariate model with synchronous observation
schemes and correlated Brownian motions of the following form: $dX\_{\ell,t} =
\sigma\_{\ell,t}dB\_{\ell,t}+b\_{\ell}(t,\omega)dt$ for $\ell=1,2$, where
$X\_{\ell}$ denotes the log-price, we are concerned with the large deviation
estimation of the vector $V\_t^n(X)=(Q\_{1,t}^n(X), Q\_{2,t}^n(X),
C\_{t}^n(X))$ where $Q\_{\ell,t}^n(X)$ and $C\_{t}^n(X)$ represente the
estimator of the quadratic variational processes
$Q\_{\ell,t}=\int\_0^t\sigma\_{\ell,s}^2ds$ and the integrated covariance
$C\_t=\int\_0^t\sigma\_{1,s}\sigma\_{2,s}\rho\_sds$ respectively, with
$\rho\_t=cov(B\_{1,t}, B\_{2,t})$. Our main motivation is to improve upon the
existing limit theorems. Our large deviations results can be used to evaluate
and approximate tail probabilities of realized (co-)volatility. As an
application we provide the large deviation for the standard dependence measures
between the two assets returns such as the realized regression coefficients up
to time $t$, or the realized correlation. Our study should contribute to the
recent trend of research on the (co-)variance estimation problems, which are
quite often discussed in high-frequency financial data analysis.
