On the implementation of multilevel Monte Carlo simulation of the stochastic volatility and interest rate model using multi-GPU clusters

We explore different methods of solving systems of stochastic differential equations by first implementing the Euler–Maruyama and Milstein methods with a Monte Carlo simulation on a CPU. The performance of the methods is significantly improved through the recently developed antithetic multilevel Monte Carlo estimator, which yields a computation complexity of 𝒪⁢(ϵ-2){\mathcal{O}(\epsilon^{-2})} root-mean-square error and does so without the approximation of Lévy areas. Further improvements in performance are gained by moving the algorithms to a GPU - first on a single device and then on a multi-GPU cluster. Our GPU implementation of the antithetic multilevel Monte Carlo displays a major speedup in computation when compared with many commonly used approaches in the literature. While our work is focused on the simulation of the stochastic volatility and interest rate model, it is easily extendable to other stochastic systems, and it is of particular interest to those with non-diagonal, non-commutative noise.