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Motivated by the results of \cite{sabanis2015}, we propose explicitEuler-type schemes for SDEs with random coefficients driven by L\'evy noisewhen the drift and diffusion coefficients can grow super-linearly. As anapplication of our results, one can construct explicit Euler-type schemes forSDEs with delays (SDDEs) which are driven by L\'evy noise and have super-linearcoefficients. Strong convergence results are established and their rate ofconvergence is shown to be equal to that of the classical Euler scheme. It isproved that the optimal rate of convergence is achieved for$\mathcal{L}^2$-convergence which is consistent with the corresponding resultsavailable in the literature.

On Explicit Approximations for L\'evy Driven SDEs with Super-linear Diffusion Coefficients