# Quantitative Finance

## What is quantitative finance?

Quantitative finance is the application of mathematics to financial problems. It has been used by economists since the 19th century. However, it wasn’t until the 1980s that it became widely accepted. Today, it is used in many different areas of finance, including trading, portfolio management, and asset pricing.

Merriam Webster Online

Definition of quantitative

• 1: of, relating to, or expressible in terms of quantity
• 2: of, relating to, or involving the measurement of quantity or amount
• 3: based on quantity
specifically, of classical verse : based on temporal quantity or duration of sounds

Wikipedia

Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling of financial markets.

In general, there exist two separate branches of finance that require advanced quantitative techniques: derivatives pricing on the one hand, and risk and portfolio management on the other. Mathematical finance overlaps heavily with the fields of computational finance and financial engineering. The latter focuses on applications and modeling, often by help of stochastic asset models, while the former focuses, in addition to analysis, on building tools of implementation for the models. Also related is quantitative investing, which relies on statistical and numerical models (and lately machine learning) as opposed to traditional fundamental analysis when managing portfolios.

## Applications of Quantitative Finance

There are several different areas where quantitative finance has been used. One of these is in the area of finance itself. For example, there are algorithms that help banks determine how much money to lend out to customers. Another application is in the area of derivatives trading. Derivatives are contracts that allow two parties to exchange assets at some point in the future. They are also known as “financial instruments” because they are often traded between companies and investors.

## History of Quantitative Finance

Quantitative Finance was first developed by mathematicians who were interested in creating new ways to model financial markets. This led to the development of the Black–Scholes equation, which is still widely used today.

## Types of Models

There are two main categories of quantitative finance models: discrete event simulation (DES) and continuous-time simulation (CTS). DES models simulate the behavior of individual market participants while CTS models simulate how the entire market behaves as a whole.