Financial Modeling - Quantitative Finance

Quantitative Finance

In quantitative finance, financial modeling entails the development of a sophisticated mathematical model. Models here deal with asset prices, market movements, portfolio returns and the like. A key distinction is between models of the financial situation of a large, complex firm or "quantitative financial management", models of the returns of different stocks or "quantitative asset pricing", models of the price or returns of derivative securities or "financial engineering" and models of the firm's financial decisions or "quantitative corporate finance". Applications include:

  • Option pricing and calculation of their "Greeks"
  • Other derivatives, especially Interest rate derivatives and Exotic derivatives
  • Modeling the term structure of interest rates (short rate modelling) and credit spreads
  • Credit scoring and provisioning
  • Corporate financing activity prediction problems
  • Portfolio problems
  • Real options
  • Risk modeling and Value at risk.

These problems are often stochastic and continuous in nature, and models here thus require complex algorithms, entailing computer simulation, advanced numerical methods (such as numerical differential equations, numerical linear algebra, dynamic programming) and/or the development of optimization models. The general nature of these problems is discussed under Mathematical finance, while specific techniques are listed under Outline of finance: Mathematical tools; see also Financial models with long-tailed distributions and volatility clustering.

Modellers are generally referred to as "quants" (quantitative analysts), and typically have advanced (Ph.D. level) backgrounds in quantitative disciplines such as physics, engineering, computer science, mathematics or operations research. Alternatively, or in addition to their quantitative background, they complete a finance masters with a quantitative orientation, such as the Master of Quantitative Finance, or the more specialized Master of Computational Finance or Master of Financial Engineering.

Although spreadsheets are widely used here also (almost always requiring extensive VBA), custom C++ or numerical analysis software such as MATLAB is often preferred, particularly where stability or speed is a concern. Matlab is the tool of choice for doing economics research because of its intuitive programming, graphical and debugging tools, but C++/Fortran are preferred for conceptually simple but high computational costs applications where Matlab is too slow. Additionally, for many (of the standard) derivative and portfolio applications, commercial software is available, and the choice as to whether the model is to be developed in-house, or whether existing products are to be deployed, will depend on the problem in question.

The complexity of these models may result in incorrect pricing or hedging or both. This Model risk is the subject of ongoing research by finance academics, and is a topic of great, and growing, interest in the risk management arena.

Criticism of the discipline (often preceding the Financial crisis of 2007-2008 by several years) emphasizes the differences between the mathematical and physical sciences and finance, and the resultant caution to be applied by modelers, and by traders and risk managers using their models. Notable here are Emanuel Derman and Paul Wilmott, authors of the Financial Modelers' Manifesto. Some go further and question whether mathematical- and statistical modeling may be applied to finance at all, at least with the assumptions usually made (for options; for portfolios). In fact, these may go so far as to question the "empirical and scientific validity... of modern financial theory". Notable here are Nassim Taleb and Benoit Mandelbrot. See also "Criticism" under Mathematical finance.

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