Traditionally, the main mathematical tools used in finance were the techniques of compound interest. However, since about the mid-1960s many other techniques have been introduced to help understand the functioning of capital markets. The valuation of options, in particular, requires special methods from stochastic calculus. Calculations of compound interest make it possible to work out how money grows, how loans are repaid and what is the value of cash flows which will be received in the future. They also make it possible to compare interest rates which may be quoted under quite different conventions. These techniques are also referred to as 'discounted cash flow' (DCF) methods.

In addition to compound interest calculations, other parts of mathematics are particularly useful in finance. Matrices make it possible to represent entire tables of data using algebraic notation, and also to describe algebraic operations on them. This has many applications in finance, particularly related to portfolios consisting of a large number of securities. Matrix algebra is also extremely convenient for describing the calculation of mean-variance efficient portfolios.

Calculus deals with calculating the rates of change of function (differentiation)(, and also the areas under curves (integration). Stochastic calculus can be used to consider the behaviour of things which evolve randomly through time such as portfolios or the valuation of call options. Finally, the tools of statistics and econometrics are fundamentally important to understanding the behaviour of and returns on securities.