An alternative to Itô's formula to solve linear financial stochastic differential equations

Abstract. 
In this paper, we present a method for solving many stochastic differential equations from finance in a very simple way without using the usual Itˆo’s formula. Our approach is straightforward and relies on using a linear ordinary differential equation method. The apparent simplicity of this method makes it attractive and accessible to a wider audience. We illustrate our approach by deriving solutions of some well-known stochastic financial models like Vasicek, Cox-Ingersoll-Ross, Hull and White, Brownian bridge, among others.