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F# for Quantitative Finance by Johan Astborg

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Learning about root-finding algorithms

In this section, we'll learn about the different methods used in numerical analysis to find the roots of functions. Root-finding algorithms are very useful, and we will learn more about their applications when we talk about volatility and implied volatility.

The bisection method

In this section, we will look at a method for finding the roots of a function using the bisection method. This method will be used later in this book to numerically find the implied volatility for an option that is given a certain market price. The bisection method uses iteration and repeatedly bisects an interval for the next iteration.

The following function implements bisection in F#:

let rec bisect n N (f:float -> float) (a:float) ...

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