Simulation in the Real World

In this paper, we propose two practicable approaches for consistently modelling the realworld and risk-neutral measures within cross-asset Monte-Carlo frameworks. We go on to explore the necessity of supporting the real-world measure and consider its calibration with the aid of an explicit example of a 3-factor Hull-White model exhibiting the volatility hump and roll-down effect. This example parallels the 1-factor lattice model considered in Hull, Sokol and White, however, allows risk-premia which are stable through time and illustrates the necessity of having a sufficiently rich correlation structure in order to produce realistic dynamic risk-premia