Differential testing is a highly effective technique for automatically detecting software bugs and vulnerabilities when the specifications involve an analysis over multiple executions simultaneously. Differential fuzzing, in particular, operates as a guided randomized search, aiming to find (similar) inputs that lead to a maximum difference in software outputs or their behaviors. However, fuzzing, as a dynamic analysis, lacks any guarantees on the absence of bugs: from a differential fuzzing campaign that has observed no bugs (or a minimal difference), what is the risk of observing a bug (or a larger difference) if we run the fuzzer for one or more steps? This paper investigates the application of Extreme Value Theory (EVT) to address the risk of missing or underestimating bugs in differential fuzzing. The key observation is that differential fuzzing as a random process resembles the maximum distribution of observed differences. Hence, EVT, a branch of statistics dealing with extreme values, is an ideal framework to analyze the tail of the differential fuzzing campaign to contain the risk. We perform experiments on a set of real-world Java libraries and use differential fuzzing to find information leaks via side channels in these libraries. We first explore the feasibility of EVT for this task and the optimal hyperparameters for EVT distributions. We then compare EVT-based extrapolation against baseline statistical methods like Markov's as well as Chebyshev's inequalities, and the Bayes factor. EVT-based extrapolations outperform the baseline techniques in 14.3% of cases and tie with the baseline in 64.2% of cases. Finally, we evaluate the accuracy and performance gains of EVT-enabled differential fuzzing in real-world Java libraries, where we reported an average saving of tens of millions of bytecode executions by an early stop.