Chapter 9. Mathematical Tools

The mathematicians are the priests of the modern world.

— Bill Gaede

Since the arrival of the so-called Rocket Scientists on Wall Street in the ’80s and ’90s,

finance has evolved into a discipline of applied mathematics. While early research papers

in finance came with few mathematical expressions and equations, current ones are mainly

comprised of mathematical expressions and equations, with some explanatory text around.

This chapter introduces a number of useful mathematical tools for finance, without

providing a detailed background for each of them. There are many useful books on this

topic available. Therefore, this chapter focuses on how to use the tools and techniques

with Python. Among other topics, it covers:

Approximation

Regression and interpolation are among the most often used numerical techniques in

finance.

Convex optimization

A number of financial disciplines need tools for convex optimization (e.g., option

pricing when it comes to model calibration).

Integration

In particular, the valuation of financial (derivative) assets often boils down to the

evaluation of integrals.

Symbolic mathematics

Python provides with SymPy a powerful tool for symbolic mathematics, e.g., to solve

(systems of) equations.