MATLAB, which derives its name from Matrix Laboratory, is a computing language that is used in India and other countries to process data in the form of arrays of numbers. MATLAB integrates computation and visualization into a flexible computer environment, and provides a diverse family of built-in functions that can be used in a straightforward manner to obtain numerical solutions to a wide range of math problems.The MATLAB editor has several features that make it especially suitable for creating scripts and functions files. But the most important advantage of MATLAB is that it is a very simple, yet powerful, programming language. Simple code means less time to develop and less chance for programming bugs. MATLAB code can exploit a wide and reliable library of numerical functions and it is much more compact. Unlike C++, users need not bother with things such as memory allocation, variable declaration, etc. MATLAB is an excellent rapid prototyping tool as well; it allows users to implement a quite complex algorithm with much less code. MATLAB toolboxes (a toolbox in MATLAB provides in-built functions for a specific domain) can be used to solve a wide array of problems. For example, the Financial Toolbox provides functions for the mathematical modelling and statistical analysis of financial data.
Math in Finance
Finance is not only about money; it involves quite a bit of mathematics and a copious amount of statistics. Financial mathematics involves combination of mathematics and modelling in order to solve financial problems. It combines tools from statistics, probability, stochastic processes and amalgamates it with the economic theory. Financial math is used by varied sectors. As an example, one instance where math has changed the derivative and option trading instruments is the Black-Scholes model (also referred to as Black-Scholes-Merton) model. It can be described as a second order partial differential equation that calculates the price of stock options over time. This model has affected the derivatives market that involves crores of Rupees of transactions per day in India. There are several such mathematical models that economists use. With mathematical tools like MATLAB at their disposal, various types of organizations and financial service providers utilize financial mathematics as part of their core operations. Various aspects of financial mathematical models – especially ones that involve statistics – are used in the retail and commercial banks, hedge funds, investment management companies and by regulatory bodies.
Math in Banking
The general perception of a layman is that the only math required for banking is arithmetic (the branch of mathematics that deals with numbers and the basic operations like addition, subtraction, multiplication, division, percentages, etc.). That is not true though. Banking is one important subset of finance and an integral part of today’s society which uses higher math. Let’s walk through a few instances where complex math is used in banking:
Cash Reserves: All banks need to maintain cash reserves as a cushion against unforeseen losses. This amount is called risk capital and regulators determine this capital by applying the theory of Coherent Risk. It works on the probabilistic model of statistics.
Financial Risk Management: Techniques for measuring risk are a prerequisite for profitability analysis. In a bank, risk is usually quantified in terms of risk capital (also called as economic capital). Some of the risks in the banking (and insurance) sector include credit risk management which is caused due to losses on bad loans when some borrowers default on repayment. Additionally, banks also need to deal with operational risk, which includes losses resulting from inadequate or failed internal processes, and fraud or litigation. The role of financial risk management is to measure and manage these risks. Probability theory and standard deviation from the math branch of statistics plays a pivotal role in analyzing these risks.
Actuarial Science: involves analyzing the financial consequences of risk using mathematical models. Actuarial modelling focuses on deterministic models and their application to financial products. This is done by applying mathematical, statistical, financial and economic theory to banking and business problems, and measuring probability so as to calculate the financial impact of undesirable events. Actuarial knowledge is useful in calculating the default probabilities of loan books in the banking sector. It also involves econometrics (the discipline of applying statistical methods to analyze economic data) in the investments that banks make.
MATLAB in Finance and Banking
From the examples above, it should be clear that high level finance and banking involves complex math. Unless and until sophisticated software is used, it is not easily possible to derive solutions to the mathematical models used in finance. The Financial Toolbox in MATLAB is one such tool. It provides functions for the mathematical modelling and statistical analysis of financial data. It enables economists to analyze, back test, and optimize investment portfolios taking into account parameters like turnover, transaction costs, semi-continuous constraints, and minimum or maximum number of assets. The Financial Toolbox in MATLAB enables economists to estimate risk, model credit scorecards, analyze yield curves, price fixed-income instruments and measure investment performance. The stochastic differential equation (SDE) tools let users model and simulate a variety of stochastic processes. Time series analysis functions lets users perform transformations or regressions with missing data and convert between different trading calendars and day-count conventions.
Central bank economists and researchers use MATLAB to prototype, validate, deploy, and share financial and economic models in support of critical policy decisions. With MATLAB, users can:
If you need more information about the benefits that MATLAB or the Financial Toolbox offers, you can get in touch with us. We are DesignTech Systems, and we are an exclusive Business Partner of MathWorks in India for MATLAB & SIMULINK suite of solutions.