When building trees to price options, we often increase the number of partitions per day, n , to improve accuracy. But increasing n often lowers efficiency. Under LARCH, raising n makes the GARCH tree grow exponentially. Lyuu and Wu (2005) prove that the criteria for explosion and non-explosion under LGARCH depend on n . Surprisingly, not all GARCH models share the same property. This thesis proves that LGARCH, NGARCH, GJR-GARCH, TS-GARCH and TGARCH share this property, but the Heston-Nandi model and VAGRCH do not.