Pricing vulnerable options under first passage model can be very difficult – especially when the default boundary depends on the option value. Analytical formula can’t be derived and numerical approaches become unstable due to nonlinearity error. This thesis provides a three dimension tree that can simultaneously simulates the evolution of the underlying asset’s value and firm’s value. The nonlinearity error problem can be alleviated by making the tree align with the default boundary and the barrier. Our tree model can evaluate the both model of Klein (1996) and Klein and Inglis (2001) and the pricing results converge to the closed form of Klein (1996.) The pricing results of vulnerable barrier option under the Merton’s model converge to the closed form of Pan (2010), too.