Wrong-way risk (WWR) arises when the value of a financial transaction is adversely correlated with the creditworthiness of the counterparty. This paper investigates WWR effects on the pricing of counterparty credit risk for interest rate instruments. These effects are captured via the correlations between the default of the counterparty and the two relevant market risk factors, namely the level and the volatility of the instantaneous spot interest rate. We consider an interest rate model featuring unspanned stochastic volatility behavior in order to analyze the effects of correlations on both volatility-insensitive instruments (interest rate swaps) and volatility-sensitive products (interest rate caps and floors). We also investigate the impact of correlation on the gap risk in collateralized instruments. Our empirical findings show that the wrong-way effect induced by the dependence between the interest rate volatility and the default intensity is generally small, even for volatility-sensitive derivatives. However, a dependence between the interest rate level and the default intensity has a sizable impact on counterparty risk.