Efficient and Exact Simulation of the Gaussian Affine Interest Rate Models (with Application to the Hull White Model and G2++ Model)

The Gaussian affine interest rate models are widely used in the financial industry for pricing, hedging and also risk management purposes. We consider the multifactor models with time dependent parameters. Usually the models are simulated using some appropriate discretization schema because the joint distribution of the stochastic and discounting factors is not known. We derive the exact joint conditional distribution of the stochastic and discounting factors. Additionally we show how an efficient and exact Monte Carlo simulation of the Hull White and G2++ interest rates models could be performed