Financial modeling
Encyclopedia
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.
, investment banking
and the accounting profession financial modelling is largely synonymous with cash flow forecasting. This usually involves the preparation of detailed company specific models used for decision making purposes and financial analysis
. Applications include:
To generalize as to the nature of these models: firstly, as they are built around financial statement
s, 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 rate
s, tax
percentage, etc…) and internal / company specific variables (wages, unit cost
s , 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.
Modellers are sometimes referred to (tongue in cheek) as "number crunchers", and are often designated as a "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 or explicit training in modeling. At the same time, numerous commercial training course
s 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, and several standardizations and "best practice
s" 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.
. Models here deal with asset prices, market movements, portfolio returns and the like. Applications include:
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 analyst
s), 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
, 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
.
, 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
.
Abstraction
Abstraction is a process by which higher concepts are derived from the usage and classification of literal concepts, first principles, or other methods....
(a model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
) of a financial
Finance
"Finance" is often defined simply as the management of money or “funds” management Modern finance, however, is a family of business activity that includes the origination, marketing, and management of cash and money surrogates through a variety of capital accounts, instruments, and markets created...
decision making
Decision making
Decision making can be regarded as the mental processes resulting in the selection of a course of action among several alternative scenarios. Every decision making process produces a final choice. The output can be an action or an opinion of choice.- Overview :Human performance in decision terms...
situation. This is a mathematical model
Mathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
designed to represent (a simplified version of) the performance of a financial asset or a portfolio, of a business, a project
Project
A project in business and science is typically defined as a collaborative enterprise, frequently involving research or design, that is carefully planned to achieve a particular aim. Projects can be further defined as temporary rather than permanent social systems that are constituted by teams...
, 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
Corporate finance
Corporate finance is the area of finance dealing with monetary decisions that business enterprises make and the tools and analysis used to make these decisions. The primary goal of corporate finance is to maximize shareholder value while managing the firm's financial risks...
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
Tradecraft
Tradecraft is a general term that denotes a skill acquired through experience in a trade.The term is also used within the intelligence community as a collective word for the techniques used in modern espionage...
, such as welding, or a science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...
- the task of financial modeling has been gaining acceptance and rigor over the years.
Accounting
In corporate financeCorporate finance
Corporate finance is the area of finance dealing with monetary decisions that business enterprises make and the tools and analysis used to make these decisions. The primary goal of corporate finance is to maximize shareholder value while managing the firm's financial risks...
, investment banking
Investment banking
An investment bank is a financial institution that assists individuals, corporations and governments in raising capital by underwriting and/or acting as the client's agent in the issuance of securities...
and the accounting profession financial modelling is largely synonymous with cash flow forecasting. This usually involves the preparation of detailed company specific models used for decision making purposes and financial analysis
Financial analysis
Financial analysis refers to an assessment of the viability, stability and profitability of a business, sub-business or project....
. Applications include:
- Business valuationBusiness valuationBusiness valuation is a process and a set of procedures used to estimate the economic value of an owner’s interest in a business. Valuation is used by financial market participants to determine the price they are willing to pay or receive to consummate a sale of a business...
, especially discounted cash flowDiscounted cash flowIn finance, discounted cash flow analysis is a method of valuing a project, company, or asset using the concepts of the time value of money...
, but including other valuation problemsValuation (finance)In finance, valuation is the process of estimating what something is worth. Items that are usually valued are a financial asset or liability. Valuations can be done on assets or on liabilities... - Scenario planningScenario planningScenario planning, also called scenario thinking or scenario analysis, is a strategic planning method that some organizations use to make flexible long-term plans. It is in large part an adaptation and generalization of classic methods used by military intelligence.The original method was that a...
and management decision making ("what is"; "what if"; "what has to be done") - Capital budgetingCapital budgetingCapital budgeting is the planning process used to determine whether an organization's long term investments such as new machinery, replacement machinery, new plants, new products, and research development projects are worth pursuing...
- Cost of capitalCost of capitalThe cost of capital is a term used in the field of financial investment to refer to the cost of a company's funds , or, from an investor's point of view "the shareholder's required return on a portfolio of all the company's existing securities"...
(i.e. WACCWeighted average cost of capitalThe weighted average cost of capital is the rate that a company is expected to pay on average to all its security holders to finance its assets....
) calculations - Financial statement analysisFinancial statement analysisFinancial statement analysis is the process of understanding the risk and profitability of a firm through analysis of reported financial information, particularly annual and quarterly reports....
(including of operating and finance leaseFinance leaseA finance lease or capital lease is a type of lease. It is a commercial arrangement where:* the lessee will select an asset ;* the lessor will purchase that asset;...
s, and R&DResearch and developmentThe phrase research and development , according to the Organization for Economic Co-operation and Development, refers to "creative work undertaken on a systematic basis in order to increase the stock of knowledge, including knowledge of man, culture and society, and the use of this stock of... - Project financeProject financeProject finance is the long term financing of infrastructure and industrial projects based upon the projected cash flows of the project rather than the balance sheets of the project sponsors...
.
To generalize as to the nature of these models: firstly, as they are built around financial statement
Financial statement
A financial statement is a formal record of the financial activities of a business, person, or other entity. In British English—including United Kingdom company law—a financial statement is often referred to as an account, although the term financial statement is also used, particularly by...
s, 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 rate
Exchange rate
In finance, an exchange rate between two currencies is the rate at which one currency will be exchanged for another. It is also regarded as the value of one country’s currency in terms of another currency...
s, tax
Tax
To tax is to impose a financial charge or other levy upon a taxpayer by a state or the functional equivalent of a state such that failure to pay is punishable by law. Taxes are also imposed by many subnational entities...
percentage, etc…) and internal / company specific variables (wages, unit cost
Unit cost
The unit cost of a product is the cost per standard unit supplied, which may be a single sample or a container of a given number. When purchasing more than a single unit, the total cost will increase with the number of units, but it is common for the unit cost to decrease as quantity is increased...
s , etc…). Correspondingly, both characteristics are reflected (at least implicitly) in the mathematical form of these models: firstly, the models are in discrete time
Discrete time
Discrete time is the discontinuity of a function's time domain that results from sampling a variable at a finite interval. For example, consider a newspaper that reports the price of crude oil once every day at 6:00AM. The newspaper is described as sampling the cost at a frequency of once per 24...
; secondly, they are deterministic.
Modellers are sometimes referred to (tongue in cheek) as "number crunchers", and are often designated as a "financial analyst
Financial analyst
A financial analyst, securities analyst, research analyst, equity analyst, or investment analyst is a person who performs financial analysis for external or internal clients as a core part of the job.-Job:...
". 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
Certified International Investment Analyst
Certified International Investment Analyst is a global finance designation offered by the Association of Certified International Investment Analysts to financial professionals; candidates may be financial analysts, portfolio managers or investment advisors...
and CFA
Chartered Financial Analyst
The Chartered Financial Analyst Program is a graduate level self-study program offered by the CFA Institute to investment and financial professionals...
generally do not provide direct or explicit training in modeling. At the same time, numerous commercial training course
Professional development
Professional development refers to skills and knowledge attained for both personal development and career advancement. Professional development encompasses all types of facilitated learning opportunities, ranging from college degrees to formal coursework, conferences and informal learning...
s are offered, both through universities and privately.
Although purpose built software
Business software
This article is about software made for business, if you were looking for the business of selling software, see Software business.Business software is generally any software program that helps a business increase productivity or measure their productivity...
does exist, the vast proportion of the market is spreadsheet
Spreadsheet
A spreadsheet is a computer application that simulates a paper accounting worksheet. It displays multiple cells usually in a two-dimensional matrix or grid consisting of rows and columns. Each cell contains alphanumeric text, numeric values or formulas...
-based - this is largely since the models are almost always company specific. Microsoft Excel
Microsoft Excel
Microsoft Excel is a proprietary commercial spreadsheet application written and distributed by Microsoft for Microsoft Windows and Mac OS X. It features calculation, graphing tools, pivot tables, and a macro programming language called Visual Basic for Applications...
now has by far the dominant position, having overtaken Lotus 1-2-3
Lotus 1-2-3
Lotus 1-2-3 is a spreadsheet program from Lotus Software . It was the IBM PC's first "killer application"; its huge popularity in the mid-1980s contributed significantly to the success of the IBM PC in the corporate environment.-Beginnings:...
in the 1990s. Spreadsheet-based modelling can have its own problems, and several standardizations and "best practice
Best practice
A best practice is a method or technique that has consistently shown results superior to those achieved with other means, and that is used as a benchmark...
s" have been proposed. "Spreadsheet risk" is increasingly studied and managed.
One critique here, is that model outputs, i.e. line items
Chart of accounts
__FORCETOC__A chart of accounts is a created list of the accounts used by a business entity to define each class of items for which money or the equivalent is spent or received...
, often incorporate “unrealistic implicit assumptions” and “internal inconsistencies” (for example, a forecast for growth in revenue but without corresponding increases in working capital
Working capital
Working capital is a financial metric which represents operating liquidity available to a business, organization or other entity, including governmental entity. Along with fixed assets such as plant and equipment, working capital is considered a part of operating capital. Net working capital is...
, fixed assets and the associated financing, may imbed unrealistic assumptions about asset turnover, leverage
Leverage (finance)
In finance, leverage is a general term for any technique to multiply gains and losses. Common ways to attain leverage are borrowing money, buying fixed assets and using derivatives. Important examples are:* A public corporation may leverage its equity by borrowing money...
and / or equity financing
Equity (finance)
In accounting and finance, equity is the residual claim or interest of the most junior class of investors in assets, after all liabilities are paid. If liability exceeds assets, negative equity exists...
). 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
Computer programming
Computer programming is the process of designing, writing, testing, debugging, and maintaining the source code of computer programs. This source code is written in one or more programming languages. The purpose of programming is to create a program that performs specific operations or exhibits a...
concepts. More serious criticism, in fact, relates to the nature of budgeting itself, and its impact on the organization.
Quantitative finance
In quantitative finance, financial modeling entails the development of a sophisticated mathematical modelMathematical model
A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used not only in the natural sciences and engineering disciplines A mathematical model is a...
. Models here deal with asset prices, market movements, portfolio returns and the like. Applications include:
- Modeling the term structure of interest rateInterest rateAn interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...
s (short rate modelShort rate modelIn the context of interest rate derivatives, a short-rate model is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,.-The short rate:...
ling) and credit spreadCredit spreadCredit spread may refer to:*Credit spread *Credit spread...
s; Interest rate derivativeInterest rate derivativeAn interest rate derivative is a derivative where the underlying asset is the right to pay or receive a notional amount of money at a given interest rate...
s - Option pricingValuation of optionsIn finance, a price is paid or received for purchasing or selling options. This price can be split into two components.These are:* Intrinsic Value* Time Value-Intrinsic Value:...
and "Greeks"Greeks (finance)In mathematical finance, the Greeks are the quantities representing the sensitivities of the price of derivatives such as options to a change in underlying parameters on which the value of an instrument or portfolio of financial instruments is dependent. The name is used because the most common of...
; other derivativesDerivative (finance)A derivative instrument is a contract between two parties that specifies conditions—in particular, dates and the resulting values of the underlying variables—under which payments, or payoffs, are to be made between the parties.Under U.S... - Credit scoring and provisioning
- PortfolioPortfolio (finance)Portfolio is a financial term denoting a collection of investments held by an investment company, hedge fund, financial institution or individual.-Definition:The term portfolio refers to any collection of financial assets such as stocks, bonds and cash...
problems - Real options
- Risk modelingRisk modelingFor risk modeling in general see risk modelingFinancial risk modeling refers to the use of formal econometric techniques to determine the aggregate risk in a financial portfolio...
and Value at riskValue at riskIn financial mathematics and financial risk management, Value at Risk is a widely used risk measure of the risk of loss on a specific portfolio of financial assets...
.
These problems are often stochastic
Stochastic
Stochastic refers to systems whose behaviour is intrinsically non-deterministic. A stochastic process is one whose behavior is non-deterministic, in that a system's subsequent state is determined both by the process's predictable actions and by a random element. However, according to M. Kac and E...
and continuous in nature, and models here thus require complex algorithms
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
, entailing computer simulation
Monte Carlo methods in finance
Monte Carlo methods are used in finance and mathematical finance to value and analyze instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining their average value over the range of resultant outcomes. This is usually done...
, advanced numerical methods (such as numerical differential equations
Numerical partial differential equations
Numerical partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations .Numerical techniques for solving PDEs include the following:...
or numerical linear algebra
Numerical linear algebra
Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers. It is often a fundamental part of engineering and computational science problems, such as image and signal processing, Telecommunication, computational...
), and / or the development of optimization models
Optimization (mathematics)
In mathematics, computational science, or management science, mathematical optimization refers to the selection of a best element from some set of available alternatives....
. 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 analyst
Quantitative analyst
A quantitative analyst is a person who works in finance using numerical or quantitative techniques. Similar work is done in most other modern industries, but the work is not always called quantitative analysis...
s), and typically have strong (Ph.D.
Ph.D.
A Ph.D. is a Doctor of Philosophy, an academic degree.Ph.D. may also refer to:* Ph.D. , a 1980s British group*Piled Higher and Deeper, a web comic strip*PhD: Phantasy Degree, a Korean comic series* PhD Docbook renderer, an XML renderer...
level) backgrounds in quantitative disciplines such as physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
, engineering
Engineering
Engineering is the discipline, art, skill and profession of acquiring and applying scientific, mathematical, economic, social, and practical knowledge, in order to design and build structures, machines, devices, systems, materials and processes that safely realize improvements to the lives of...
, computer science
Computer science
Computer science or computing science is the study of the theoretical foundations of information and computation and of practical techniques for their implementation and application in computer systems...
, mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
or operations research
Operations research
Operations research is an interdisciplinary mathematical science that focuses on the effective use of technology by organizations...
. Alternatively, or in addition to their quantitative background, they complete a finance masters
Master of Finance
A Master of Finance is a Master's degree designed to prepare graduates for careers in financial analysis, investment management and corporate finance. An alternate degree title is Master in Finance or Master of Science in Finance...
with a quantitative orientation, such as the Master of Quantitative Finance
Master of Quantitative Finance
A masters degree in quantitative finance concerns the application of mathematical methods to the solution of problems in financial economics. There are several like-titled degrees which may further focus on financial engineering, financial risk management, computational finance and/or mathematical...
, 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
Visual Basic for Applications
Visual Basic for Applications is an implementation of Microsoft's event-driven programming language Visual Basic 6 and its associated integrated development environment , which are built into most Microsoft Office applications...
), custom C++
C++
C++ is a statically typed, free-form, multi-paradigm, compiled, general-purpose programming language. It is regarded as an intermediate-level language, as it comprises a combination of both high-level and low-level language features. It was developed by Bjarne Stroustrup starting in 1979 at Bell...
or numerical analysis software such as MATLAB
MATLAB
MATLAB is a numerical computing environment and fourth-generation programming language. Developed by MathWorks, MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages,...
is often preferred, particularly where stability or speed is a concern. Additionally, for many (of the standard) derivative and portfolio applications, commercial software
Commercial software
Commercial software, or less commonly, payware, is computer software that is produced for sale or that serves commercial purposes.Commercial software is most often proprietary software, but free software packages may also be 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
Hedge (finance)
A hedge is an investment position intended to offset potential losses that may be incurred by a companion investment.A hedge can be constructed from many types of financial instruments, including stocks, exchange-traded funds, insurance, forward contracts, swaps, options, many types of...
or both. This Model risk
Model risk
In finance, model risk is the risk involved in using models to value financial securities. Rebonato considers alternative definitions including:...
is the subject of ongoing research by finance academics, and is a topic of great, and growing, interest in the risk management
Risk management
Risk management is the identification, assessment, and prioritization of risks followed by coordinated and economical application of resources to minimize, monitor, and control the probability and/or impact of unfortunate events or to maximize the realization of opportunities...
arena.
Criticism
Criticism
Criticism is the judgement of the merits and faults of the work or actions of an individual or group by another . To criticize does not necessarily imply to find fault, but the word is often taken to mean the simple expression of an objection against prejudice, or a disapproval.Another meaning of...
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
Emanuel Derman
Emanuel Derman is a South African-born academic, businessman and writer. He is best known as a quantitative analyst, and author of the book My Life as A Quant: Reflections on Physics and Finance....
and Paul Wilmott
Paul Wilmott
Paul Wilmott is a researcher, consultant and lecturer in quantitative finance. He is best known as the author of various academic and practitioner texts on risk and derivatives, and for Wilmott magazine and Wilmott.com , a quantitative finance portal....
, authors of the Financial Modelers' Manifesto
Financial Modelers' Manifesto
The Financial Modelers' Manifesto was a proposal for more responsibility in risk management and quantitative finance written by financial engineers Emanuel Derman and Paul Wilmott. The manifesto includes a Modelers' Hippocratic Oath...
. 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
Financial economics
Financial Economics is the branch of economics concerned with "the allocation and deployment of economic resources, both spatially and across time, in an uncertain environment"....
". Notable here are Nassim Taleb and Benoit Mandelbrot
Benoît Mandelbrot
Benoît B. Mandelbrot was a French American mathematician. Born in Poland, he moved to France with his family when he was a child...
.
History
Much effort has gone into the study of financial markets and how prices vary with time. Charles DowCharles Dow
Charles Henry Dow was an American journalist who co-founded Dow Jones & Company with Edward Jones and Charles Bergstresser....
, one of the founders of Dow Jones & Company
Dow Jones & Company
Dow Jones & Company is an American publishing and financial information firm.The company was founded in 1882 by three reporters: Charles Dow, Edward Jones, and Charles Bergstresser. Like The New York Times and the Washington Post, the company was in recent years publicly traded but privately...
and The Wall Street Journal
The Wall Street Journal
The Wall Street Journal is an American English-language international daily newspaper. It is published in New York City by Dow Jones & Company, a division of News Corporation, along with the Asian and European editions of the Journal....
, enunciated a set of ideas on the subject which are now called Dow Theory
Dow Theory
The Dow theory on stock price movement is a form of technical analysis that includes some aspects of sector rotation. The theory was derived from 255 Wall Street Journal editorials written by Charles H. Dow , journalist, founder and first editor of the Wall Street Journal and co-founder of Dow...
. This is the basis of the so-called technical analysis
Technical analysis
In finance, technical analysis is security analysis discipline for forecasting the direction of prices through the study of past market data, primarily price and volume. Behavioral economics and quantitative analysis incorporate technical analysis, which being an aspect of active management stands...
method of attempting to predict future changes. One of the tenets of "technical analysis" is that market trends
Market trends
A market trend is a putative tendency of a financial market to move in a particular direction over time. These trends are classified as secular for long time frames, primary for medium time frames, and secondary for short time frames...
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
Random walk hypothesis
The random walk hypothesis is a financial theory stating that stock market prices evolve according to a random walk and thus the prices of the stock market cannot be predicted. It is consistent with the efficient-market 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
Volatility (finance)
In finance, volatility is a measure for variation of price of a financial instrument over time. Historic volatility is derived from time series of past market prices...
. In 1900, Louis Bachelier
Louis Bachelier
-External links:** Louis Bachelier webpage at the Université de Franche-Comté, Besançon / France. Text in French.** also from Index Funds Advisors, this discussion of...
modeled the time series
Time series
In statistics, signal processing, econometrics and mathematical finance, a time series is a sequence of data points, measured typically at successive times spaced at uniform time intervals. Examples of time series are the daily closing value of the Dow Jones index or the annual flow volume of the...
of changes in the logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...
of stock prices as a random walk
Random walk
A random walk, sometimes denoted RW, is a mathematical formalisation of a trajectory that consists of taking successive random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the...
in which the short-term changes had a finite variance
Variance
In probability theory and statistics, the variance is a measure of how far a set of numbers is spread out. It is one of several descriptors of a probability distribution, describing how far the numbers lie from the mean . In particular, the variance is one of the moments of a distribution...
. 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
Benoît Mandelbrot
Benoît B. Mandelbrot was a French American mathematician. Born in Poland, he moved to France with his family when he was a child...
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
Power law
A power law is a special kind of mathematical relationship between two quantities. When the frequency of an event varies as a power of some attribute of that event , the frequency is said to follow a power law. For instance, the number of cities having a certain population size is found to vary...
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
Standard deviation
Standard deviation is a widely used measure of variability or diversity used in statistics and probability theory. It shows how much variation or "dispersion" there is from the average...
.
See also
- Economic model
- Financial engineering
- Financial forecastFinancial forecastA financial forecast is normally an estimate of future financial outcomes for a company or country . Using historical internal accounting and sales data, in addition to external market and economic indicators, a financial forecast is an economist's best guess of what will happen to a company in...
- Financial Modelers' ManifestoFinancial Modelers' ManifestoThe Financial Modelers' Manifesto was a proposal for more responsibility in risk management and quantitative finance written by financial engineers Emanuel Derman and Paul Wilmott. The manifesto includes a Modelers' Hippocratic Oath...
- Financial planning
- Integrated business planningIntegrated business planningIntegrated business planning refers to the technologies, applications and processes of connecting the planning function across the enterprise to improve organizational alignment and financial performance...
- Model auditModel AuditA model audit is the colloquial term for the tasks performed when conducting due diligence on a financial model, in order to eliminate spreadsheet error. . A study in 1998 concluded that even MBA students with over 250 hours of spreadsheet development experience had a 24% chance of introducing...
- Modeling and analysis of financial markets
External links
- 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