Chapter 5: Linear Systems and PDEs

In this chapter we present several methods for solving linear systems of the form Ax=b.

Here A is a (m x m) matrix and both x and b are m-dimensional vectors.

Our interest in linear systems is related to the solution of PDEs and therefore we will consider the case where the coefficient matrix A is tridiagonal.

As concrete examples will have

1. Plain Vanilla Call in the Black-Scholes Model (VBA);
2. Plain Vanilla Call in the Square-Root Model (VBA);
3. Pricing American Options with the Crank-Nicolson Scheme (VBA);
4. Pricing a Double Barrier Call in the BS Model (MATLAB and VBA);
5. Pricing an Option on a Coupon Bond in the Cox-Ingersoll-Ross Model (MATLAB).

Files

Zipped VBA files