Computational finance

Computational finance is a branch of applied mathematics that studies problems of practical interest in finance. Some slightly different definitions are the study of data and algorithms currently used in finance and the mathematics of computer programs that realize financial models or systems.

Computational finance emphasizes practical numerical methods rather than mathematical proofs and focuses on techniques that apply directly to economic analyses. It is an interdisciplinary field between mathematical finance and numerical methods. Two major areas are efficient and accurate computation of fair values of financial securities and the modeling of stochastic price series.

History

The field of computational finance emerged in the 1970s. Early computational finance was focused on pricing derivatives and calculating risk in a static setting. This led to the development of a large number of sophisticated mathematical tools such as Monte Carlo methods, finite difference methods, and binomial trees.

Mathematical tools

Computational finance makes heavy use of sophisticated mathematical models and numerical solutions. Some of the mathematical tools used in computational finance are:

• Stochastic calculus
• Partial differential equations
• Monte Carlo methods
• Numerical linear algebra
• Optimization

Applications

Computational finance has been applied to a number of areas in finance including:

• Option pricing
• Risk management
• Portfolio optimization
• Asset and liability management
• Financial engineering
• High-frequency trading

See also

• Quantitative analyst
• Financial modeling
• Mathematical finance
• Computational economics