Mastering Python for Finance - Second Edition

A down-and-out option

Let's take a look at an example of a down-and-out option. At any time during the life of the option, should the underlying asset price fall below an S_barrier barrier price, the option is considered worthless. Since, in the grid, the finite difference scheme represents all the possible price points, we only need to consider nodes with the following price range:

We can then set up the boundary conditions as follows: