- Financial modeling
Financial modeling is the task of building an abstract representation (a model) of a financial decision making situation. This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or a portfolio, of a business, a project, or any other investment. Financial modeling is a general term that means different things to different users; the reference usually relates either to accounting and corporate finance applications, or to quantitative finance applications. While there has been some debate in the industry as to the nature of financial modeling - whether it is a tradecraft, such as welding, or a science - the task of financial modeling has been gaining acceptance and rigor over the years. Several scholarly books have been written on the topic, in addition to numerous scientific articles.
In corporate finance, investment banking and the accounting profession (and generally in Europe ), financial modelling is largely synonymous with cash flow forecasting. This usually involves the preparation of detailed company specific models used for decision making purposes; see Financial analysis. Applications include:
- Business valuation, especially discounted cash flow, but including other valuation problems
- Scenario planning and management decision making ("what is"; "what if"; "what has to be done" ).
- Capital budgeting
- Cost of capital (i.e. WACC) calculations
- Financial statement analysis (including of Operating - and Finance leases, and R&D )
- Project finance.
To generalize as to the nature of these models: firstly, as they are built around financial statements, calculations and outputs are monthly, quarterly or annual; secondly, the inputs take the form of “assumptions”, where the analyst specifies the values that will apply in each period for external / global variables (exchange rates, tax percentage, etc…) and internal / company specific variables (wages, unit costs , etc…). Correspondingly, both characteristics are reflected (at least implicitly) in the mathematical form of these models: firstly, the models are in discrete time; secondly, they are deterministic.  For discussion of the issues that may arise, see below; for dicussion as to more sophisticated approaches sometimes employed, see Corporate finance: Quantifying uncertainty.
Modellers are sometimes referred to (tongue in cheek) as "Number crunchers", and are often designated as "Financial analyst". Typically, the modeller will have completed an MBA or MSF with (optional) coursework in "financial modeling". Accounting qualifications, and finance certifications such as the CIIA and CFA,  generally do not provide direct / explicit training in modeling. At the same time, numerous commercial training courses are offered,   both through universities and privately.
Although purpose built software does exist, the vast proportion of the market is spreadsheet-based - this is largely since the models are almost always company specific. Microsoft Excel now has by far the dominant position, having overtaken Lotus 1-2-3 in the 1990s.
Spreadsheet-based modelling can have its own problems  ("Spreadsheet Shortcomings"), and several standardizations and "best practices" have been proposed. "Spreadsheet risk" is increasingly studied and managed.
One critique here, is that model outputs, i.e. line items, often incorporate “unrealistic implicit assumptions” and “internal inconsistencies”  (for example, a forecast for growth in revenue but without corresponding increases in working capital, fixed assets and the associated financing, may imbed unrealistic assumptions about asset turnover, leverage and / or equity financing). What is required, but often lacking, is that all key elements are explicitly and consistently forecasted. An extension of this is that modellers often additionally "fail to identify crucial assumptions" relating to inputs, "and to explore what can go wrong". Here, in general, modellers "use point values and simple arithmetic instead of probability distributions and statistical measures" - i.e., as mentioned, the problems are treated as deterministic in nature - and thus calculate a single value for the asset or project, but without providing information on the range, variance and sensitivity of outcomes; . Other critiques discuss the lack of adequate spreadsheet design skills, and of basic computer programming concepts.  (More serious criticism, in fact, relates to the nature of budgeting itself, and its impact on the organization. )
In quantitative finance (and generally in the U.S. ), financial modeling entails the development of a sophisticated mathematical model. Models here deal with asset prices, market movements, portfolio returns and the like. Applications include:
- Modeling the term structure of interest rates (short rate modelling) and credit spreads; Interest rate derivatives
- Option pricing and "Greeks"; other derivatives
- Credit scoring and provisioning
- 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 or numerical linear algebra), and / or the development of optimization models. The general nature of these problems is discussed below, while specific techniques are listed under Outline of finance: Mathematical tools.
Modellers are generally referred to as "quants" (quantitative analysts), and typically have strong (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.  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 ; see 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 .
Much effort has gone into the study of financial markets and how prices vary with time. Charles Dow, one of the founders of Dow Jones & Company and The Wall Street Journal, enunciated a set of ideas on the subject which are now called Dow Theory. This is the basis of the so-called technical analysis method of attempting to predict future changes. One of the tenets of "technical analysis" is that market trends give an indication of the future, at least in the short term. The claims of the technical analysts are disputed by many academics, who claim that the evidence points rather to the random walk hypothesis, which states that the next change is not correlated to the last change.
The scale of changes in price over some unit of time is called the volatility. In 1900, Louis Bachelier modeled the time series of changes in the logarithm of stock prices as a random walk in which the short-term changes had a finite variance. This causes longer-term changes to follow a Gaussian distribution.
Modeling the changes by distributions with finite variance is now known to be inappropriate. In the 1960s it was discovered by Benoît Mandelbrot that changes in prices do not follow a Gaussian distribution, but are rather modeled better by Lévy alpha-stable distributions. The scale of change, or volatility, depends on the length of the time interval to a power a bit more than 1/2. Large changes up or down are more likely than what one would calculate using a Gaussian distribution with an estimated standard deviation.
- Economic model
- Financial engineering
- Financial forecast
- Financial Modelers' Manifesto
- Financial planning
- Integrated business planning
- Model audit
- Modeling and analysis of financial markets
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- Benninga, Simon (2006). Principles of Finance with Excel. New York: Oxford University Press. ISBN 0-195-30150-1.
- Brigo, Damiano; Fabio Mercurio (2006). Interest Rate Models - Theory and Practice with Smile, Inflation and Credit, 2nd Edition. London. ISBN 978-3-540-22149-4.
- Clewlow, Les; Chris Strickland (1998). Implementing Derivative Models. New Jersey: Wiley. ISBN 0471966517.
- Day, Alastair (2007). Mastering Financial Modelling in Microsoft Excel. London: Pearson Education. ISBN 0-273-70806-6.
- Fabozzi, Frank J. (1998). Valuation of fixed income securities and derivatives, 3rd Edition. Hoboken, NJ: Wiley. ISBN 978-1-883249-25-0.
- Fabozzi, Frank J.; Sergio M. Focardi, Petter N. Kolm (2004). Financial Modeling of the Equity Market: From CAPM to Cointegration. Hoboken, NJ: Wiley. ISBN 0-471-69900-4.
- Fusai, Gianluca; Andrea Roncoroni (2008). Implementing Models in Quantitative Finance: Methods and Cases. London: Springer Finance. ISBN 3540223487.
- Haug, Espen (2006). The Complete Guide to Option Pricing Formulas. New York: McGraw-Hill. ISBN 0071389970.
- Ho, Thomas; Sang Bin Lee (2004). The Oxford Guide to Financial Modeling. New York: Oxford University Press . ISBN 978-0195169621.
- Jackson, Mary; Mike Staunton (2001). Advanced modelling in finance using Excel and VBA. New Jersey: Wiley. ISBN 0471499226.
- Jondeau, Eric; Ser-Huang Poon, Michael Rockinger (2007). Financial Modeling Under Non-Gaussian Distributions. London: Springer. ISBN 1-846-28419-9.
- Ongkrutaraksa, Worapot (2006). Financial Modeling and Analysis: A Spreadsheet Technique for Financial, Investment, and Risk Management, 2nd Edition. Frenchs Forest: Pearson Education Australia. ISBN 0-733-98474-6.
- Proctor, Scott (2009). Building Financial Models with Microsoft Excel: A Guide for Business Professionals, 2nd Edition. Hoboken, NJ: Wiley. ISBN 978-0-470-48174-5.
- Swan, Jonathan (2007). Financial Modelling Special Report. London: Institute of Chartered Accountants in England & Wales.
- Swan, Jonathan (2008). Practical Financial Modelling, 2nd Edition. London: CIMA Publishing. ISBN 0-750-68647-2.
- Tjia, John (2003). Building Financial Models. New York: McGraw-Hill. ISBN 0-071-40210-1.
- Vladimirou, Hercules (2007). Financial Modeling. Norwell, MA: Springer. ISBN 0-585-13223-2.
- Mantegna, Rosario N.; Kertesz, Janos (2010). "Focus on Statistical Physics Modelling in Economics and Finance". New Journal of Physics. http://iopscience.iop.org/1367-2630/focus/Focus%20on%20Statistical%20Physics%20Modelling%20in%20Economics%20and%20Finance.
- ^ Nassim Nicholas Taleb (2007). The Black Swan: The Impact of the Highly Improbable. Random House. ISBN 978-1-4000-6351-2.
- Best Practice: Spreadsheet Modelling Standards, Spreadsheet Standards Review Board
- Best Practice, European Spreadsheet Risks Interest Group
- FAST Modeling Standard, The FAST Modelling Standard
- Eliminating Risks in Spreadsheets A useful article on how to avoid common spreadsheet modeling errors
- Best practice of financial modelling - An article for finance professionals by Arixcel Ltd
- Articles on Financial Modeling by Pristine - A useful set of blog articles and free financial models (open sourced) by Pristine
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