A volatility decomposition control variate technique for Monte Carlo simulations of Heath, Jarrow, Morton models

The aim of this work is to develop a simulation approach to the yield curve evolution in the Heath, Jarrow and Morton framework. The stochastic quantities considered as affecting the forward rate volatility function are the spot rate and the forward rate. A decomposition of the volatility function into a Hull and White volatility and a remainder allows us to develop an efficient Control Variate Method that makes use of the closed form solution of the Hull and White call option. This technique considerably speeds up the simulation algorithm to approximate call option values with Monte Carlo simulation.