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This paper introduces ARCHModels.jl, a package for the Julia programming language that implements a number of univariate and multivariate autoregressive conditional heteroskedasticity models. This model class is the workhorse tool for modeling the conditional volatility of financial assets. The distinguishing feature of these models is that they model the latent volatility as a (deterministic) function of past returns and volatilities. This recursive structure results in loop-heavy code which, due to its just-in-time compiler, Julia is well-equipped to handle. As such, the entire package is written in Julia, without any binary dependencies. We benchmark the performance of ARCHModels.jl against popular implementations in MATLAB, R, and Python, and illustrate its use in a detailed case study.