zero-coupon bond option

In this paper a combination of two financial derivatives in financial markets modelled of future interest rates is presented and evaluated. In fact European option pricing is driven when zero-coupon bond is considered as underlying asset in a market under Hull-White model . For this purpose, the exact solutions of the valuation of this bond option are driven, using Lie group symmetries method. Then in the next part, the finite difference method is applied to find numerical solutions for assumed bond option pricing. Then the significance and usefulness of this approximated method is comparing with the exact solutions by some plotted graphs.