Chapter 9. Mathematical Tools
The mathematicians are the priests of the modern world.
— Bill Gaede
Since the arrival of the socalled 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 withSymPy
a powerful tool for symbolic mathematics, e.g., to solve (systems of) equations.
Approximation
To begin with, let us import the libraries that we need for the moment—NumPy
and matplotlib.pyplot
:
In
[
1
]:
import
numpy
as
np
import
matplotlib.pyplot
as
plt
%
matplotlib
inline
Throughout this discussion, the main example function ...
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