# Financial Mathematics

The application of mathematics and mathematical modeling to solve financial problems

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## What is Financial Mathematics?

Financial mathematics describes the application of mathematics and mathematical modeling to solve financial problems. it is sometimes referred to as quantitative finance, financial engineering, and computational finance. The discipline combines tools from statistics, probability, and stochastic processes and combines it with economic theory.

### Mathematics and Statistics Explained

Mathematics is the discipline of academics that involves the study of quantity, structure, space, and change by using formulas and mathematical proofs to provide insight or make predictions about nature.

The study of mathematics has led to completely new disciplines within academia, including the field of statistics. Statistics refers to the discipline that is concerned with analyzing data and applying insights gathered from the data to solve various scientific, industrial, or even social problems. It has become an essential discipline as technology continues to evolve.

Statistics is used prominently in academic papers, as a crucial part of science is making testable hypotheses and proving or contradicting said hypotheses. It plays an integral role in that process. In addition, it is used to develop groundbreaking technologies, such as machine learning, leading to even more specialized disciplines in finance, such as:

• Actuarial science – The study of assessing risk in insurance and finance
• Data mining – Applying statistics and data pattern recognition to solve problems
• Data science – The discipline of using scientific methods to extract knowledge from data
• Econometrics – The discipline of applying statistical methods to analyze economic data

### Prominence of Financial Mathematics

The use of mathematics and statistics within the field of finance has been increasing substantially in the past, and such a trend is expected to continue. Various types of organizations and financial service providers utilize financial mathematics as part of their core operations, such as:

• Investment banks
• Retail and commercial banks
• Hedge funds
• Investment management companies
• Corporate treasuries
• Regulatory bodies

In addition, financial mathematics is applied considerably to solve problems, such as:

• Derivative security pricing and valuation
• Portfolio creation and structuring
• Quantitative investing strategies
• Risk management

As the markets seek to become more efficient, quantitative methods will continue to be adopted. Over the long history of financial markets, the concepts of valuation and pricing, as well as optimizing capital allocation, have been important problems to observe within the capital markets.

Quantitative finance was developed as a specialized field within economics to tackle the problems of the valuation of assets and financial instruments, as well as optimizing capital allocation and resources. Over centuries, fundamental theories about the overall economy and valuation of assets have been developed through the mathematical models.

The models describe the relationships between various economic variables, such as prices, market movements, volatility, and interest rates. By using quantitative tools, more accurate conclusions can be drawn from the economic variables.

### Example: Black-Scholes-Merton Model

For example, the Black-Scholes-Merton (BSM) Model is a mathematical model that is used for pricing options. Options are a particular form of derivative, which is a financial asset that derives its value from the price of another underlying asset.

Before the Black-Scholes Merton model was developed, the pricing of options contracts was extremely difficult and limited. However, with the model, financial academics and professionals alike could accurately price the complicated derivative products.

It is one of the most important financial models ever developed and is still used today to price options. The three professors – Fischer Black, Myron Scholes, and Robert Merton – won a Nobel Prize for the development of the model.

### Criticism of Financial Mathematics

Financial mathematics has grown and become significantly more prominent within financial markets. However, the increasing complexity of mathematical models and quantitative strategies have drawn criticisms. The criticisms peaked during the Global Financial Crisis in 2008.

Critics argue that the blind reliance on the models, especially by many finance professionals who do not understand the underlying concepts, can lead to disastrous outcomes for the economy.

However, the use of quantitative principles within finance will continue to be prominent. Markets seek to become more efficient over time – just as stock trading once went from the transfer of physical certificates to the transfer of electronic certificates. More quantitative practices and strategies will be developed to make markets more efficient and help investors generate alpha. They include applications such as: