Financial modeling

'''Financial modeling''' <ref name = "IBM">[https://www.ibm.com/think/topics/financial-modeling What is Financial Modeling?], IBM</ref> is the task of building an abstract representation (a model) of a real world financial situation.<ref name="iop">{{Cite web |author = Investopedia Staff| url=http://www.investopedia.com/terms/f/financialmodeling.asp | title=Financial Modeling|date = 2020}}</ref> This is a mathematical model designed to represent (a simplified version of) the performance of a financial asset or portfolio of a business, project, or any other investment.

Typically, then, financial modeling is understood to mean an exercise in either asset pricing or corporate finance of a quantitative nature. It involves translating a set of hypotheses about the behavior of markets or agents into numerical predictions.<ref name="sciencedirect.com">{{cite journal|last1=Low|first1=R.K.Y.|last2=Tan|first2=E. |title=The Role of Analysts' Forecasts in the Momentum Effect|journal=International Review of Financial Analysis|volume=48|pages=67–84|date=2016|doi=10.1016/j.irfa.2016.09.007|url=https://espace.library.uq.edu.au/view/UQ:406166/UQ406166_OA.pdf}}</ref>  At the same time, "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.

==Accounting== [[File:Cash Flow Projection.png|thumb|Spreadsheet-based Cash Flow Projection (click to view at full size)]] In corporate finance and the accounting profession, ''financial modeling'' typically entails financial statement forecasting; usually the preparation of detailed company-specific models used for <ref name=iop/> decision making purposes, valuation and financial analysis. <ref name = "IBM"/> In entrepreneurial and investment contexts, financial models are widely used to illustrate business viability and capital requirements for funding discussions.<ref>[https://qubit.capital/blog/how-to-create-a-financial-model-that-secures-funding How to Create a Financial Model That Secures Funding], Qubit Capital Blog (2024)</ref>

Applications include: *Business valuation, stock valuation, and project valuation - especially via discounted cash flow, but including other valuation approaches *Scenario planning, FP&A and management decision making ("what is"; "what if"; "what has to be done"<ref name="SiegelShim1997">See §39 "Corporate Planning Models" and §294 "Simulation Model" in: {{cite book|author1=Joel G. Siegel|author2=Jae K. Shim|author3=Stephen Hartman|title=Schaum's quick guide to business formulas: 201 decision-making tools for business, finance, and accounting students|url=https://books.google.com/books?id=4JpojQPk8YsC|access-date=12 November 2011|date=1 November 1997|publisher=McGraw-Hill Professional|isbn=978-0-07-058031-2}}</ref>) *Budgeting: revenue forecasting and analytics; production budgeting; operations budgeting *Capital budgeting, including cost of capital (i.e. WACC) calculations *Cash flow forecasting; working capital- and treasury management; asset and liability management *Financial statement analysis / ratio analysis (including of operating- and finance leases, and R&D) *Transaction analytics: M&A, PE, VC, LBO, IPO, Project finance,<ref>See for example: {{Cite web |title=Renewable Energy Financial Model |url=https://courses.renewablesvaluationinstitute.com/pages/academy/financial-model-user-guide |access-date=2023-03-19 |website=Renewables Valuation Institute |language=en}}</ref> P3 *Credit decisioning: Credit analysis, Consumer credit risk; impairment- and provision-modeling *Management accounting: Activity-based costing, Profitability analysis, Cost analysis, Whole-life cost, Managerial risk accounting *Public sector procurement<ref>Confidential disclosure of a financial model is often requested by purchasing organizations undertaking public sector procurement in order that the government department can understand and if necessary challenge the pricing principles which underlie a bidder's costs. E.g. First-tier Tribunal, [https://www.bailii.org/uk/cases/UKFTT/GRC/2010/2010_0073.html Department for Works and Pensions v. Information Commissioner], UKFTT EA_2010_0073, paragraph 58, decided 20 September 2010, accessed 11 January 2024</ref>

To generalize {{Citation needed|date=November 2011}} 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....; may be thought of as the model ''parameters''), and for 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 discussion as to more sophisticated approaches sometimes employed, see {{section link|Corporate finance|Quantifying uncertainty}} and {{section link|Financial economics|Corporate finance theory}}.

Modelers are often designated "financial analyst" (and are sometimes referred to, tongue in cheek, as "number crunchers"). Typically,<ref name="Fairhurst"/> the modeler will have completed an MBA or MSF with (optional) coursework in "financial modeling".<ref>Example course: [https://study.unisa.edu.au/courses/013613/2022 Financial Modelling], University of South Australia</ref> Accounting qualifications and finance certifications such as the CIIA and CFA generally do not provide direct or explicit training in modeling.<ref name="ft">[https://www.ft.com/content/db7a4838-1352-11e5-ad26-00144feabdc0 ''The MiF can offer an edge over the CFA''] Financial Times, June 21, 2015.</ref> At the same time, numerous commercial training courses are offered, both through universities and privately. For the components and steps of business modeling here, see {{slink|Outline of finance|Financial modeling}}; see also {{section link|Valuation using discounted cash flows|Determine cash flow for each forecast period}} for further discussion and considerations.

Although purpose-built business software does exist, the vast proportion of the market is spreadsheet-based; this is largely since the models are almost always company-specific. Also, analysts will each have their own criteria and methods for financial modeling.<ref>See for example, [https://ssrn.com/abstract=256987 Valuing Companies by Cash Flow Discounting: Ten Methods and Nine Theories], Pablo Fernandez: University of Navarra - IESE Business School</ref> 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,<ref>Danielle Stein Fairhurst (2009). [http://www.fimodo.com/2009/11/six-reasons-your-spreadsheet-is-not-a-financial-model/ Six reasons your spreadsheet is NOT a financial model] {{webarchive|url=https://web.archive.org/web/20100407003951/http://www.fimodo.com/2009/11/six-reasons-your-spreadsheet-is-not-a-financial-model/|date=2010-04-07}}, fimodo.com</ref> and several standardizations and "best practice"s have been proposed.<ref name="EuSpRIG3">[http://www.eusprig.org/best-practice.htm Best Practice] {{Webarchive|url=https://web.archive.org/web/20180329184059/http://www.eusprig.org/best-practice.htm|date=2018-03-29}}, European Spreadsheet Risks Interest Group</ref> Here, professional guidelines emphasize transparent, auditable, and well-documented models. Good practice includes separating input, calculation, and output sheets to enhance traceability and reduce error risk.<ref>[https://www.pwc.com.au/deals/assets/pwc-global-financial-modeling-guidelines-booklet-live.pdf PwC Global Financial Modeling Guidelines] (2023)</ref><ref>[https://fminstitute.com/modeling-resources/financial-modeling-best-practices/ Financial Modeling Institute – Best Practices] (2023)</ref> Practical training providers further highlight consistent formatting, clear labeling, and documentation of assumptions as essential for usability and stakeholder confidence.<ref>[https://corporatefinanceinstitute.com/resources/financial-modeling/free-financial-modeling-guide/ CFI – Free Financial Modeling Guide] (2024)</ref><ref>[https://www.icaew.com/technical/business/financial-management/financial-modelling-and-forecasting ICAEW – Financial Modelling and Forecasting Guidance] (2023)</ref> "Spreadsheet risk" is increasingly studied and managed;<ref name="EuSpRIG3" /> see model audit.

One critique here, is that model ''outputs'', i.e. line items, often inhere "unrealistic implicit assumptions" and "internal inconsistencies".<ref name="PalepuHealy2007">{{cite book|author1=Krishna G. Palepu|author2=Paul M. Healy|author3=Erik Peek|author4=Victor Lewis Bernard|title=Business analysis and valuation: text and cases|url=https://books.google.com/books?id=DPK43Sku2PsC&pg=261|access-date=12 November 2011|year=2007|publisher=Cengage Learning EMEA|isbn=978-1-84480-492-4|pages=261–}}</ref> (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, debt level and/or equity financing. See {{section link|Sustainable growth rate|From a financial perspective}}.) What is required, <ref name = "IBM"/> but often lacking, is that all key elements are explicitly and consistently forecasted. Related to this, is that modellers often additionally "fail to identify crucial assumptions" relating to ''inputs'', "and to explore what can go wrong".<ref name="BrealeyMyers2003">{{cite book|author1=Richard A. Brealey|author2=Stewart C. Myers|author3=Brattle Group|title=Capital investment and valuation|url=https://books.google.com/books?id=eKF8IBCwfy4C&pg=PA223|access-date=12 November 2011|year=2003|publisher=McGraw-Hill Professional|isbn=978-0-07-138377-6|pages=223–}}</ref> Here, in general, modellers "use point values and simple arithmetic instead of probability distributions and statistical measures"<ref>Peter Coffee (2004). [http://www.eweek.com/c/a/Database/Spreadsheets-25-Years-in-a-Cell/ ''Spreadsheets: 25 Years in a Cell''], EWeek.</ref> — 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;<ref>Prof. Aswath Damodaran. [http://pages.stern.nyu.edu/~adamodar/pdfiles/papers/probabilistic.pdf ''Probabilistic Approaches: Scenario Analysis, Decision Trees and Simulations''], NYU Stern Working Paper</ref> <ref name="savage">[http://www.analycorp.com/uncertainty/flawarticle.htm The Flaw of Averages] {{webarchive|url=https://web.archive.org/web/20111207025740/http://www.analycorp.com/uncertainty/flawarticle.htm |date=2011-12-07 }}, Prof. Sam Savage, Stanford University.</ref> see {{section link|Valuation using discounted cash flows |Determine equity value}}. A further, more general critique relates to the lack of basic computer programming concepts amongst modelers, <ref>Blayney, P. (2009). [https://www.learntechlib.org/p/31495/ Knowledge Gap? Accounting Practitioners Lacking Computer Programming Concepts as Essential Knowledge]. In G. Siemens & C. Fulford (Eds.), Proceedings of World Conference on Educational Multimedia, Hypermedia and Telecommunications 2009 (pp. 151-159). Chesapeake, VA: AACE.</ref> with the result that their models are often poorly structured, and difficult to maintain. Serious criticism is also directed at the nature of budgeting, and its impact on the organization.<ref>Loren Gary (2003). [http://hbswk.hbs.edu/item/3623.html ''Why Budgeting Kills Your Company''] {{Webarchive|url=https://web.archive.org/web/20151029213855/http://hbswk.hbs.edu/item/3623.html |date=2015-10-29 }}, Harvard Management Update, May 2003.</ref><ref>Michael Jensen (2001). [https://ssrn.com/abstract=321520 ''Corporate Budgeting Is Broken, Let's Fix It''], Harvard Business Review, pp. 94-101, November 2001.</ref>

==Quantitative finance== [[File:OAS valuation tree (es).png|thumb|Visualization of an interest rate "tree" - usually returned by commercial derivatives software]]

In quantitative finance, ''financial modeling'' entails the development of a sophisticated mathematical model.<ref name="SIAM">See discussion here: {{cite web |url=https://www.siam.org/Portals/0/Student%20Programs/Thinking%20of%20a%20Career/brochure.pdf |archive-url=https://web.archive.org/web/20190305095047/https://www.siam.org/Portals/0/Student%20Programs/Thinking%20of%20a%20Career/brochure.pdf |archive-date=2019-03-05 |url-status=live |title=Careers in Applied Mathematics|publisher=Society for Industrial and Applied Mathematics}}</ref> Models here deal with asset prices, market movements, portfolio returns and the like.  Relatedly, applications include: *Option pricing and calculation of their "Greeks" ( accommodating volatility surfaces - via local / stochastic volatility models - and multi-curves) *Other derivatives, especially interest rate derivatives, credit derivatives and exotic derivatives *Credit valuation adjustment, CVA, as well as the various XVA *Modeling the term structure of interest rates (bootstrapping / multi-curves, short-rate models, HJM framework) and any related credit spread *Credit risk, counterparty credit risk, and regulatory capital: EAD, PD, LGD, PFE, EE; Jarrow–Turnbull model, Merton model, KMV model *Portfolio optimization<ref>See for example: {{cite journal|last1=Low|first1=R.K.Y.|last2=Faff|first2=R.|last3=Aas|first3=K.|title=Enhancing mean–variance portfolio selection by modeling distributional asymmetries|journal=Journal of Economics and Business|volume=85|pages=49–72|date=2016|doi=10.1016/j.jeconbus.2016.01.003|url=https://espace.library.uq.edu.au/view/UQ:377912/UQ377912_OA.pdf}}; {{cite journal|last1=Low|first1=R.K.Y.|last2=Alcock|first2=J.|last3=Faff|first3=R.|last4=Brailsford|first4=T.|title=Canonical vine copulas in the context of modern portfolio management: Are they worth it?|journal=Journal of Banking & Finance|date=2013|volume=37|issue=8|pages=3085–3099|doi= 10.1016/j.jbankfin.2013.02.036|s2cid=154138333 |url=https://espace.library.uq.edu.au/view/UQ:297895/EC15UQ297895.pdf}}</ref> and Quantitative investing more generally; see further re optimization methods employed. *Credit scoring and provisioning; Credit scorecards and {{slink|IFRS 9|Impairment}} *Structured product design and manufacture *Financial risk modeling: value at risk (parametric- and / or historical, CVaR, EVT), stress testing, "sensitivities" analysis (Greeks, duration, convexity, DV01, KRD, CS01, JTD) *Corporate finance applications:<ref name="Shimko">See David Shimko (2009). [https://web.archive.org/web/20100717072252/http://www.qfinance.com/financial-risk-management-best-practice/quantifying-corporate-financial-risk?full Quantifying Corporate Financial Risk]. archived 2010-07-17.</ref> cash flow analytics,<ref>See for example [https://brainly.in/question/7072253 this problem] (from John Hull's ''Options, Futures, and Other Derivatives''), discussing cash position modeled stochastically.</ref> corporate financing activity prediction problems, and risk analysis in capital investment *Real options *Actuarial applications: Dynamic financial analysis (DFA), UIBFM, investment modeling

These problems are generally 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 {{section link|Mathematical finance|History: Q versus P}}, while specific techniques are listed under {{section link|Outline of finance|Mathematical tools}}. For further discussion here see also: Brownian model of financial markets; Martingale pricing; Financial models with long-tailed distributions and volatility clustering; Extreme value theory; Historical simulation (finance).

Modellers are generally referred to as "quants", i.e. quantitative analysts (or "rocket scientists") and typically have advanced (Ph.D. level) backgrounds in quantitative disciplines such as statistics, 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,<ref name="Joshi">Mark S. Joshi, [http://www.markjoshi.com/downloads/advice.pdf ''On Becoming a Quant''] {{Webarchive|url=https://web.archive.org/web/20120114045604/http://www.markjoshi.com/downloads/advice.pdf |date=2012-01-14 }}.</ref> such as the Master of Quantitative Finance, or the more specialized Master of Computational Finance or Master of Financial Engineering; the CQF certificate is increasingly common.

Although spreadsheets are widely used here also (almost always requiring extensive VBA); custom C++, Fortran or Python, or numerical-analysis software such as MATLAB, are often preferred,<ref name="Joshi"/> particularly where stability or speed is a concern. MATLAB is often used at the research or prototyping stage <ref>[https://www.mathworks.com/solutions/finance-and-risk-management.html MATLAB for Quantitative Finance and Risk Management], MathWorks</ref> because of its intuitive programming, graphical and debugging tools, but C++/Fortran are preferred for conceptually simple but high computational-cost applications where MATLAB is too slow; Python is increasingly used due to its simplicity, and large standard library / available applications, including QuantLib. 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.<ref name="Joshi"/> See {{slink|Quantitative analysis (finance)|Library quantitative analysis}}.

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.<ref>Riccardo Rebonato (N.D.). [http://www.quarchome.org/ModelRisk.pdf ''Theory and Practice of Model Risk Management''].</ref>

Criticism of the discipline (often preceding the 2008 financial crisis by several years) emphasizes the differences between finance and the mathematical / physical sciences, and stresses 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 the mathematical- and statistical modeling techniques usually applied to finance are appropriate (see the assumptions made for options and for portfolios). In fact, these may go so far as to question the "empirical and scientific validity... of modern financial theory".<ref>Nassim Taleb (2009).[http://www.fooledbyrandomness.com/Triana-fwd.pdf "History Written By The Losers"], Foreword to Pablo Triana's ''Lecturing Birds How to Fly'' {{ISBN|978-0470406755}}</ref> Notable here are Nassim Taleb and Benoit Mandelbrot.<ref>{{cite web |url=http://www.fooledbyrandomness.com/fortune.pdf |title=How the Finance Gurus Get Risk All Wrong |access-date=2010-06-15 |url-status=dead |archive-url=https://web.archive.org/web/20101207045925/http://www.fooledbyrandomness.com/fortune.pdf |archive-date=2010-12-07|author = Nassim Taleb and Benoit Mandelbrot}}</ref> See also {{section link|Mathematical finance|Criticism}}, {{section link|Financial economics|Challenges and criticism}} and {{slink|Financial engineering|Criticisms}}. <!-- commenting out bullet-lists ==Use of Financial Modeling== * Historical analysis of a company * Projecting a company’s financial performance * Project finance * Real estate investments * Oil & Gas projects * Banks & Financial Institutions * Personal finances * Non-profit organizations * Government * Investment banking * Equity research

==Users of Financial Modeling== There are four main groups of users that use financial models. * Business owners and entrepreneurs * Finance and Accounting professionals * Financial Modelers and Consultants * Individuals for personal finance

==Types of Financial Models== * Discounted Cash Flow model * [http://www.streetofwalls.com/articles/investment-banking/recruiting-interviewing/comparative-company-analysis/ Comparative Company Analysis model] * [http://cpadvocates.in/Dynamicimages/260_1_905634838426559052500.pdf Sum-of-the-parts model] * Leveraged Buy Out (LBO) model * Mergers & Acquisitions (M&A) model * Industry-specific financial model * Option pricing model * Corporate finance models

==Key Consideration for Successful Financial Modeling== * Modeler should be good in Accounting, Finance and Valuation and financial modeling Excel skills. * An answer must be there for the question “What problem is this model going to solve?” * The scope, benefits, and limitations of financial modeling must be known by the modeler. * The input must be object-oriented and considering the principle “Garbage in garbage out”. * Model should be simple, easy to understand and flexible enough to accommodate future revisions. * Time management is a key aspect in financial modeling and the model should not be overwhelmed by numbers and calculation part in spreadsheets. * Model must support decision making.

==Practical Use of Financial Modeling== * Forecasting future raw material needs * Valuation of a security * Benefits of a merger * Check the size of the market opportunity * See the roadmap to profitability * Check investment requirement * Quantify and predict risk * Portfolio performance * Identify undervalued securities -->

== Competitive modeling == Several financial modeling competitions exist, emphasizing speed and accuracy in modeling. The Microsoft-sponsored ModelOff Financial Modeling World Championships were held annually from 2012 to 2019, with competitions throughout the year and a finals championship in New York or London. After its end in 2020, several other modeling championships have been started, including the Financial Modeling World Cup and Microsoft Excel Collegiate Challenge, also sponsored by Microsoft.<ref name="Fairhurst">{{Cite book|last=Fairhurst|first=Danielle Stein|url=https://books.google.com/books?id=X_9REAAAQBAJ|title=Financial Modeling in Excel for Dummies|publisher=John Wiley & Sons|year=2022 |isbn=978-1-119-84451-8|location=|oclc=1264716849}}</ref>

== Philosophy of financial modeling == Philosophy of financial modeling is a branch of philosophy concerned with the foundations, methods, and implications of modeling science.

In the philosophy of financial modeling, scholars have more recently begun to question the generally held assumption that financial modelers seek to represent any "real-world" or actually ongoing investment situation. Instead, it has been suggested that the task of the financial modeler resides in demonstrating the possibility of a transaction in a prospective investment scenario, based on a limited set of possibility conditions initially assumed in the model.<ref name="Mebius">{{cite journal |last= Mebius |first= A. |year= 2023 |title= On the epistemic contribution of financial models |journal= Journal of Economic Methodology |volume = 30 | issue = 1 |pages= 49–62 |doi= 10.1080/1350178X.2023.2172447|s2cid= 256438018 |doi-access= free }}</ref>

==See also== {{div col |colwidth=30em}} *All models are wrong *Asset pricing model *Economic model *Financial engineering *Financial forecast *Financial Modelers' Manifesto *Financial models with long-tailed distributions and volatility clustering *Financial planning *Integrated business planning *Model audit *Modeling and analysis of financial markets *{{section link|Outline of finance |Education}} *{{section link|Pro forma|Financial statements}} *Profit model *Return on modeling effort *{{slink|Unreasonable ineffectiveness of mathematics#Economics and finance}} {{div col end}}

==References == {{Reflist}}

==Bibliography==  {{refbegin|30em}} '''General''' *{{cite book | author=Avon, Jack | title=The Financial Modellers VBA Compendium | publisher=Begawans Veranda | location=London | year=2017| isbn=978-0-9956-7254-3}} *{{cite book | author=Benninga, Simon | title=Financial Modeling | url=https://archive.org/details/financialmodelin00benn | url-access=registration | publisher=MIT Press | location=Cambridge, MA | year=1997| isbn=0-585-13223-2}} *{{cite book | author=Benninga, Simon | title=Principles of Finance with Excel | publisher=Oxford University Press | location=New York | year=2006 | isbn=0-19-530150-1}} *{{cite book | last=Fabozzi | author-link=Frank Fabozzi | first=Frank J. | title=Encyclopedia of Financial Models| publisher=Wiley | location=Hoboken, NJ | year=2012| isbn=978-1-118-00673-3}} *{{cite book | last=Ho | author-link=Thomas Ho (finance) | first=Thomas|author2=Sang Bin Lee | title=The Oxford Guide to Financial Modeling| publisher=Oxford University Press | location=New York| year=2004 | isbn=978-0-19-516962-1 | author2-link=Sang Bin Lee}} *{{cite book | author=Sengupta, Chandan| title=Financial Analysis and Modeling Using Excel and VBA, 2nd Edition | publisher=John Wiley & Sons | location=Hoboken, NJ | year=2009| isbn=9780470275603}} *{{cite book | author=Winston, Wayne | title=Microsoft Excel 2013 Data Analysis and Business Modeling | publisher=Microsoft Press | year=2014| isbn=978-0735669130}} *{{Cite book | last = Yip | first = Henry | title = Spreadsheet Applications to securities valuation and investment theories | publisher = John Wiley and Sons Australia Ltd. | isbn = 0470807962 | date = 2005 }}

'''Corporate finance''' *{{cite book | author=Avon, Jack. | title=The Handbook of Financial Modeling |edition= 2nd | url=https://link.springer.com/book/10.1007/978-1-4842-6540-6| publisher=Springer | location=New York | year=2021 | doi=10.1007/978-1-4842-6540-6 | isbn=978-1-4842-6540-6 | s2cid=227164870 }} *{{cite book | last=Bastick | first=Liam | title=Introduction to Financial Modeling| publisher=Wiley | year=2020| isbn=978-1615470662}} *{{cite book | author=Beech, G. and Thayser, D. | title=Valuations, Mergers and Acquisitions | url=https://global.oup.com/academic/product/valuations-mergers-and-acquisitions-9780199052776| publisher=Oxford University Press | location=Oxford | year=2015| isbn=978-0-585-13223-5}} *{{cite book | author=Day, Alastair | title=Mastering Financial Modelling in Microsoft Excel | publisher=Pearson Education | location=London | year=2007 | isbn=978-0-273-70806-3}} *{{Cite book|author=Fairhurst, Danielle|url=https://books.google.com/books?id=X_9REAAAQBAJ&pg=PA120|title=Financial Modeling in Excel for Dummies|publisher=John Wiley & Sons|year=2022 |isbn=978-1-119-84451-8|location=|page=120|oclc=1264716849}} *{{cite book | author=Lynch, Penelope | title=Financial Modelling for Project Finance, 2nd Edition| publisher=Euromoney Trading | year=1997| isbn=9781843745488}} *{{cite book | author1= Mayes, Timothy R. |author2=Shank, Todd M. | title=Financial Analysis with Microsoft Excel| publisher=Cengage Learning | location=Boston| year=2014 | isbn= 978-1-285-43227-4|edition=7th}} *{{cite book | author=Peter K Nevitt |author2=Frank J. Fabozzi | title=Project Financing| publisher=Euromoney Institutional Investor PLC | year=2000 | isbn=978-1-85564-791-6 }} *{{cite book | author=Ongkrutaraksa, Worapot | title=Financial Modeling and Analysis: A Spreadsheet Technique for Financial, Investment, and Risk Management, 2nd Edition | publisher=Pearson Education Australia | location=Frenchs Forest | year=2006 | isbn=0-7339-8474-6}} *{{cite book | author= Palepu, Krishna G. |author2=Paul M. Healy | title= Business Analysis and Valuation Using Financial Statements, 5th Edition | publisher=South-Western College Publishing | location=Boston| year=2012| isbn= 978-1111972288}} *{{cite book | author=Pignataro, Paul | title=Financial Modeling and Valuation: A Practical Guide to Investment Banking and Private Equity | publisher=Wiley | location=Hoboken, NJ| year=2003 | isbn=978-1118558768}} *{{cite book | author=Proctor, Scott | title=Building Financial Models with Microsoft Excel: A Guide for Business Professionals, 2nd Edition | publisher=Wiley | location=Hoboken, NJ | year=2009 | isbn=978-0-470-48174-5}} *{{cite book | author= Rees, Michael | title= Financial Modelling in Practice: A Concise Guide for Intermediate and Advanced Level| publisher=Wiley | location=Hoboken, NJ | year=2008| isbn=978-0-470-99744-4}} *{{cite book | author= Rees, Michael | title= The Essentials of Financial Modeling in Excel: A Concise Guide to Concepts and Methods| publisher=Wiley | location=Hoboken, NJ | year=2023| isbn=978-1394157785}} *{{cite book | author=Soubeiga, Eric | title=Mastering Financial Modeling: A Professional's Guide to Building Financial Models in Excel | publisher=McGraw-Hill | location=New York | year=2013| isbn=978-0071808507}} *{{cite book | author=Swan, Jonathan | title=Financial Modelling Special Report | publisher=Institute of Chartered Accountants in England & Wales | location=London | year=2007 }} *{{cite book | author=Swan, Jonathan | title=Practical Financial Modelling, 2nd Edition | publisher=CIMA Publishing | location=London | year=2008 | isbn=978-0-7506-8647-1}} *{{cite book | author= Tham, Joseph|author2=Ignacio Velez-Pareja| title= Principles of Cash Flow Valuation: An Integrated Market-Based Approach | publisher=Elsevier | location=Amsterdam | year=2004 | isbn= 0-12-686040-8 }} *{{cite book | author=Tjia, John | title=Building Financial Models | publisher=McGraw-Hill | location=New York | year=2003 | isbn=0-07-140210-1}}

'''Quantitative finance''' *{{cite book | author= Hirsa, Ali| title=Computational Methods in Finance| publisher=CRC Press | location= Boca Raton| year=2013| isbn=9781439829578}} * {{Cite book |last=Blatter, Anja |last2=Bradbury, Sean |last3=Bruhn, Pascal |last4=Ernst, Dietmar |title=Risk Management in Banks and Insurance Companies |publisher=Springer |year=2025|isbn= 978-3-031-42835-7}} *{{cite book | author=Brooks, Robert | title=Building Financial Derivatives Applications with C++| publisher=Praeger | location=Westport | year=2000 | isbn=978-1567202878 }} *{{cite book | last=Brigo | author-link=Damiano Brigo | first=Damiano |author2=Fabio Mercurio | title=Interest Rate Models - Theory and Practice with Smile, Inflation and Credit| edition= 2nd | publisher= Springer Finance | location=London | year=2006| isbn=978-3-540-22149-4| author2-link=Fabio Mercurio }} *{{cite book | last=Clewlow| first=Les|author2=Chris Strickland | title=Implementing Derivative Models| publisher=Wiley | location=New Jersey| year=1998| isbn=0-471-96651-7}} *{{cite book | author=Duffy, Daniel | title=Financial Instrument Pricing Using C++ | publisher=Wiley | location=New Jersey| year=2004 | isbn=978-0470855096}} *{{cite book | last=Fabozzi | author-link=Frank Fabozzi | first=Frank J. | title=Valuation of fixed income securities and derivatives, 3rd Edition | publisher=Wiley | location=Hoboken, NJ | year=1998| isbn=978-1-883249-25-0}} *{{cite book | last=Fabozzi | first=Frank J. |author2=Sergio M. Focardi |author3=Petter N. Kolm | title=Financial Modeling of the Equity Market: From CAPM to Cointegration | publisher=Wiley | location=Hoboken, NJ | year=2004 | isbn=0-471-69900-4}} *{{Cite book | author = Shayne Fletcher | author2 = Christopher Gardner | title = Financial Modelling in Python | publisher = John Wiley and Sons | isbn = 978-0-470-74789-6 | date = 2010 }} *{{cite book | last=Fusai| first=Gianluca |author2=Andrea Roncoroni | title=Implementing Models in Quantitative Finance: Methods and Cases| publisher=Springer Finance | location=London | year=2008| isbn=978-3-540-22348-1}} *{{cite book | author= Haug, Espen Gaarder| title=The Complete Guide to Option Pricing Formulas, 2nd edition | publisher=McGraw-Hill | year=2007 | isbn=978-0071389976}} *{{cite book | title = Interest Rate Modelling in the Multi-Curve Framework | author =M. Henrard | year = 2014 | isbn =978-1137374653 | publisher = Springer}} *{{cite book | author=Hilpisch, Yves| title=Derivatives Analytics with Python: Data Analysis, Models, Simulation, Calibration and Hedging| publisher=Wiley | location=New Jersey | year=2015 | isbn=978-1-119-03799-6 }} *{{cite book | last=Jackson | first=Mary |author2=Mike Staunton| title=Advanced modelling in finance using Excel and VBA| publisher=Wiley | location=New Jersey| year=2001 | isbn=0-471-49922-6}} *{{cite book | last=Jondeau | first=Eric |author2=Ser-Huang Poon |author3=Michael Rockinger | title=Financial Modeling Under Non-Gaussian Distributions | publisher=Springer | location=London | year=2007 | isbn=978-1849965996 }} *{{cite book | author1=Joerg Kienitz|author2=Daniel Wetterau| title= Financial Modelling: Theory, Implementation and Practice with MATLAB Source| publisher=Wiley | location=Hoboken, NJ | year=2012 | isbn=978-0470744895}} *{{cite book | last= Kwok | first= Yue-Kuen | title= Mathematical Models of Financial Derivatives, 2nd edition | publisher= Springer Finance | location= London | year=2008| isbn= 978-3540422884}} *{{cite book | author=Levy, George | title=Computational Finance: Numerical Methods for Pricing Financial Instruments| publisher=Butterworth-Heinemann | year=2004 | isbn=978-0750657228 }} *{{cite book | author=London, Justin | title=Modeling Derivatives in C++ | publisher=Wiley | location=New Jersey| year=2004 | isbn=978-0471654643}} *{{cite book |author1=Löeffler, G |author2=Posch, P. | title= Credit Risk Modeling using Excel and VBA| publisher=Wiley | location= Hoboken, NJ | year=2011 | isbn= 978-0470660928 }} *{{cite book | last= Rouah | first= Fabrice Douglas |author2=Gregory Vainberg | title= Option Pricing Models and Volatility Using Excel-VBA | publisher=Wiley | location=New Jersey| year=2007| isbn= 978-0471794646 }} *{{cite book | author= Antoine Savine and Jesper Andreasen | title=Modern Computational Finance: Scripting for Derivatives and xVA| publisher=Wiley| year=2018| isbn=978-1119540786}} *{{cite book | author= Alexander Sokol | title=Long-Term Portfolio Simulation - For XVA, Limits, Liquidity and Regulatory Capital| publisher=Risk Books| year=2014| isbn=978-1782720959}} * {{Cite book |last=Charles Tapiero |title=Risk and Financial Management: Mathematical and Computational Methods |publisher=John Wiley & Son |year=2004 |isbn=0-470-84908-8}} *{{cite book | author1= Humphrey Tung |author2= Donny Lai| author3=Michael Wong|author4 = Stephen Ng | title= Professional Financial Computing Using Excel and VBA | publisher= John Wiley & Sons| year=2010| isbn= 9780470824399 }}  {{refend}} {{Corporate finance and investment banking}}

Category:Financial models Category:Actuarial science Category:Mathematical finance Category:Corporate finance Category:Computational fields of study