Markovian and multi-curve friendly parametrisation of HJM model used in valuation adjustment of interest rate derivatives

We consider feasible Heath-Jarrow-Morton framework specifications that are easily implementable in XVA engines when pricing linear and non-linear interest rate derivatives in multicurve environment. Our particular focus is on relatively less liquid markets (Polish PLN) and the calibration problems arising from that fact. We first develop necessary tool-kit for multicurve construction and XVA integration and then show and discuss various specifications of HJM model with regard to their practical usage. We demonstrate the importance of Cheyette subclass and derive dynamics of instantaneous forward rates in generic form. We performed calibrations of several one-factor models of that form and found out that even with relativelysimple specification i.e. Hull-White with two summands we may achieve satisfactory results in terms of calibration's quality and calculation time.