  In this work we want to provide a general principle to evaluate the CVA
(Credit Value Adjustment) for a vulnerable option, that is an option subject to
some default event, concerning the solvability of the issuer. CVA is needed to
evaluate correctly the contract and it is particularly important in presence of
WWR (Wrong Way Risk), when a credit deterioration determines an increase of the
claim's price. In particular, we are interested in evaluating the CVA in
stochastic volatility models for the underlying's price (which often fit quite
well the market's prices) when admitting correlation with the default event. By
cunningly using Ito's calculus, we provide a general representation formula
applicable to some popular models such as SABR, Hull \& White and Heston, which
explicitly shows the correction in CVA due to the processes correlation. Later,
we specialize this formula and construct its approximation for the three
selected models. Lastly, we run a numerical study to test the formula's
accuracy, comparing our results with Monte Carlo simulations.
