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This paper develops a novel weak multilevel Monte-Carlo (MLMC) approximationscheme for L\'evy-driven Stochastic Differential Equations (SDEs). The schemeis based on the state space discretization (via a continuous-time Markov chainapproximation) of the pure-jump component of the driving L\'evy process and isparticularly suited if the multidimensional driver is given by a L\'evy copula.The multilevel version of the algorithm requires a new coupling of theapproximate L\'evy drivers in the consecutive levels of the scheme, which isdefined via a coupling of the corresponding Poisson point processes. Themultilevel scheme is weak in the sense that the bound on the level variances isbased on the coupling alone without requiring strong convergence. Moreover, thecoupling is natural for the proposed discretization of jumps and is easy tosimulate. The approximation scheme and its multilevel analogous are applied toexamples taken from mathematical finance, including the pricing of credit,equity and interest rate derivatives.

A weak MLMC scheme for L\'evy-copula-driven SDEs with applications to the pricing of credit, equity and interest rate derivatives