In this chapter we introduce a number of algorithms to solve nonlinear equations and to find the minimum value of a function in one unknown variable. This is called univariate root finding and minimisation, respectively. We reduce the scope to functions of a single variable and to the computation of implied volatility. There are enough topics to consider even for this seemingly simple problem.
The goals are:
We examine the twin topics of computing the roots of functions and function minimisation and subsequent implementation in C++. Some of the advantages are that we are employing a defined process to create a software framework to solve problems, as introduced in Chapter 9.
Some of the benefits that this chapter delivers are: