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