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:
- 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).
- In particular, the valuation of financial (derivative) assets often boils down to the evaluation of integrals.
- Symbolic mathematics
SymPya powerful tool for symbolic mathematics, e.g., to solve (systems of) equations.
To begin with, let us import the libraries that we need for the moment—
Throughout this discussion, the main example function ...