Quantitative finance – also referred to as “mathematical finance” – includes those finance activities where a sophisticated mathematical model is required, and thus overlaps several of the above.

As a specialized practice area, quantitative finance comprises primarily three sub-disciplines; the underlying theory and techniques are discussed in the next section:

DCF valuation formula widely applied in business and finance, since articulated in 1938. Here, to get the value of the firm, its forecasted free cash flows are discounted to the present using the weighted average cost of capital for the discount factor.

For share valuation investors use the related dividend discount model.

Financial economics is the branch of economics that studies the interrelation of financial variables, such as prices, interest rates and shares, as opposed to real economic variables, i.e. goods and services.

It thus centers on pricing, decision making, and risk management in the financial markets, and produces many of the commonly employed financial models. (Financial econometrics is the branch of financial economics that uses econometric techniques to parameterize the relationships suggested.)

The discipline has two main areas of focus:

asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital; respectively:

Financial mathematics is the field of applied mathematics concerned with financial markets.

As above, in terms of practice, the field is referred to as quantitative finance and / or mathematical finance, and comprises primarily the three areas discussed.