I will use the Hull-White model to simulate interest rates (for the pricing of interest rate derivatives and a Black-Scholes framework with stochastic interest rates). The first idea was to use the exact solution, so I could circumvent the simulation with small timesteps which is needed e.g. with Euler-Maruyama. But a problem appeared in the calculation of the zero bond prices. The integral over the short rates involved, forced me again to use small timesteps within the simulation. So the question came up why I do not directly simulate the zero bond prices, where the exact distribution is also known. Has anyone ideas or suggestions, concerning pros and cons?Thanks a lot in advance!