The multi-curve extension of Heath−Jarrow−Morton framework is a popular method for pricing interest rate derivatives and overnight indexed swaps in the post-crisis financial market. That is, the set of forward curves is represented as a solution to a boundary value problem for an infinite-dimensional stochastic differential equation. In this paper, we review the post-crisis market proxies for interest rate models. Then, we consider a simple model that belongs to the above framework. This model is driven by a single Wiener process, and we discretize the space of trajectories of its driver by cubature method on Wiener space. After that, we discuss possible methods for numerical solution of the resulting deterministic boundary value problem in the finite dimensional case. Finally, we compare and contrast the obtained numerical solutions of cubature method and classical Monte Carlo simulation.