We consider risk-neutral valuation of a contingent claim under bilateral counterparty risk using the well-known reduced-form approach. Probabilistic valuation formulas derived under this framework cannot be used for practical pricing due to their recursive path dependencies. By imposing restrictions on the dynamics of the risk-free rate and stochastic intensities of counterparties’ default times, we develop path-independent probabilistic valuation formulas that have closed-form solutions or can lead to computationally efficient pricing schemes. Our framework also incorporates wrong-way risk (WWR). Advancing the work of Ghamami and Goldberg, we derive calibration- implied formulas that enable us to compare derivatives values in the presence and absence of WWR. We illustrate that derivatives values under WWR need not be less than derivatives values in the absence of WWR. A sufficient condition under which this inequality holds is when the price process follows a semimartingale with independent increments.