# Numerical Differentiation

## Document Type

Book Chapter

## Publication Title

Indian Statistical Institute Series

## Abstract

Derivatives arise in finance in several situations. In option pricing, the hedge ratios are related to the derivatives, also known as Greeks. We have seen the need for one such Greek, namely vega, in Sect. 3.3. Another important application is sensitivity analysis. The general idea is to understand how a target variable, like stock price, is affected by an input variable like book value of the company. A particular sensitivity is bond duration, where the input variable is interest rate and the target variable is bond price. Given any differentiable function, we can find its derivative analytically. However, in many situations, we might need or prefer to obtain a numerical approximation. Here are some examples: The exact formula, even if available in closed analytical form, may entail evaluation of complicated functions. In such cases numerical approximations might be simpler and quicker to obtain. It is often the case that the form of the underlying function is unknown, but given any argument, it can be evaluated. In such cases, even though there is an underlying differentiable function, we cannot find the analytical derivative.

## First Page

47

## Last Page

52

## DOI

10.1007/978-981-19-2008-0_5

## Publication Date

1-1-2023

## Recommended Citation

Sen, Rituparna and Das, Sourish, "Numerical Differentiation" (2023). *Book Chapters*. 201.

https://digitalcommons.isical.ac.in/book-chapters/201