Black-Scholes: diferenças entre revisões
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O modelo de Black-Scholes do mercado para um ativo faz as seguintes suposições explícitas:
* É possível emprestar e tomar emprestado a uma [[taxa de juros livre de risco]] constante e conhecida.
* O preço segue um [[movimento Browniano geométrico]] com tendência (drift) e [[Volatilidade (finanças)|volatilidade]] constantes.
* Não há custos de transação.
* A ação não paga dividendos (veja [[#Instrumentos que pagam dividendos discretos proporcionais|abaixo]] para extensões que aceitem pagamento de dividendos).
* Não há restrições para a [[venda a descoberto]].
O modelo trata apenas [[opções europeias]]. A partir dessas condições ideais no mercado para um ativo (e para a opção sobre o ativo), os autores mostram que o valor de uma opção (a fórmula de Black-Scholes) varia apenas com o preço da ação e com o tempo até o vencimento.
Linha 287:
O parâmetro ''u'' que aparece no modelo de dividendos discretos não é o mesmo que o parâmetro<math> \mu</math> que aparece em outros lugares no artigo. Para relações entre eles veja [[Movimento Browniano Geométrico]].
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===Referências primárias===
* {{cite journal|title=The Pricing of Options and Corporate Liabilities|last=Black|first=Fischer|coauthors=Myron Scholes|journal=Journal of Political Economy|date=1973|volume=81|issue=3|pages=637–654|doi=10.1086/260062}} [http://links.jstor.org/sici?sici=0022-3808%28197305%2F06%2981%3A3%3C637%3ATPOOAC%3E2.0.CO%3B2-P] (Black and Scholes' original paper.)
* {{cite journal|title=Theory of Rational Option Pricing|last=Merton|first=Robert C.|journal=Bell Journal of Economics and Management Science|date=1973|volume=4|issue=1|pages=141–183|doi=10.2307/3003143}} [http://links.jstor.org/sici?sici=0005-8556%28197321%294%3A1%3C141%3ATOROP%3E2.0.CO%3B2-0&origin=repec]
===Aspectos históricos e sociológicos===
* {{cite book|title=Capital Ideas: The Improbable Origins of Modern Wall Street|last=Bernstein|first=Peter|authorlink=Peter L. Bernstein|year=1992|isbn=0-02-903012-9|publisher=The Free Press}}
* {{cite journal|title=An Equation and its Worlds: Bricolage, Exemplars, Disunity and Performativity in Financial Economics|last=MacKenzie|first=Donald|journal=Social Studies of Science|date=2003|volume=33|issue=6|pages=831–868|doi=10.1177/0306312703336002}} [http://sss.sagepub.com/cgi/content/abstract/33/6/831]
* {{cite journal|title=Constructing a Market, Performing Theory: The Historical Sociology of a Financial Derivatives Exchange|last=MacKenzie|first=Donald|coauthors=Yuval Millo|journal=American Journal of Sociology|date=2003|volume=109|issue=1|pages=107–145|doi=10.1086/374404}} [http://www.journals.uchicago.edu/AJS/journal/issues/v109n1/060259/brief/060259.abstract.html]
* {{cite book|title=An Engine, not a Camera: How Financial Models Shape Markets|last=MacKenzie|first=Donald|
isbn=0-262-13460-8|publisher=MIT Press|year=2006}}
=={{Ligações externas}}==
;Discussão do modelo
* {{Link|en|2=http://www.mayin.org/ajayshah/PDFDOCS/Shah1997_bms.pdf |3=Black, Merton, and Scholes: Their work and its consequences}}, by Ajay Shah
* {{Link|en|2=http://www.portfolio.com/news-markets/national-news/portfolio/2008/02/19/Black-Scholes-Pricing-Model?print=true |3=Inside Wall Street's Black Hole}} by [[Michael Lewis]], March 2008 Issue of portfolio.com
* {{Link|en|2=http://www.forbes.com/opinions/2008/04/07/black-scholes-options-oped-cx_ptp_0408black.html |3=Whither Black-Scholes?}} by Pablo Triana, April 2008 Issue of Forbes.com
;Derivação e solução
* {{Link||2=http://knol.google.com/k/marc-samuel-delvarello/the-black-scholes-formula/34hdx7ks0jha3/108?hd=ns |3=Proving the Back-Scholes formula}}
* {{Link||2=http://www.quantnotes.com/fundamentals/options/riskneutrality.htm |3=The risk neutrality derivation of the Black-Scholes Equation}}, quantnotes.com
* {{Link||2=http://www.quantnotes.com/fundamentals/options/black-scholes.htm |3=Arbitrage-free pricing derivation of the Black-Scholes Equation}}, quantnotes.com, or [http://www.sjsu.edu/faculty/watkins/blacksch.htm an alternative treatment], Prof. Thayer Watkins
* {{Link||2=http://www.quantnotes.com/fundamentals/options/solvingbs.htm |3=Solving the Black-Scholes Equation}}, quantnotes.com
* {{Link||2=http://www.physics.uci.edu/%7Esilverma/bseqn/bs/bs.html |3=Solution of the Black–Scholes Equation Using the Green's Function}}, Prof. Dennis Silverman
* {{Link||2=http://homepages.nyu.edu/~sl1544/KnownClosedForms.pdf |3=Solution via risk neutral pricing or via the PDE approach using Fourier transforms}} (includes discussion of other option types), Simon Leger
* {{Link||2=http://planetmath.org/encyclopedia/AnalyticSolutionOfBlackScholesPDE.html |3=Step-by-step solution of the Black-Scholes PDE}}, planetmath.org.
* {{Link||2=http://www.opentradingsystem.com/quantNotes/Black_Scholes_formula_.html |3=Black-Scholes formula}}
;Revisitando o modelo
* {{Link||2=http://www.findarticles.com/p/articles/mi_m3937/is_1996_March-April/ai_18367627 |3=Anomalies in option pricing: the Black–Scholes model revisited}}, New England Economic Review, March-April, 1996
* {{Link||2=http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1012075 |3=Why We Have Never Used the Black-Scholes-Merton Option Pricing Formula}}, [[Nassim Taleb]] and [[Espen Haug]]
* {{Link||2=http://www.ederman.com/new/docs/qf-Illusions-dynamic.pdf |3=The illusions of dynamic replication}}, [[Emanuel Derman]] and [[Nassim Taleb]]
* {{Link||2=http://www.ederman.com/new/docs/risk-non_continuous_hedge.pdf |3=When You Cannot Hedge Continuously: The Corrections to Black-Scholes}}, [[Emanuel Derman]]
* {{Link||2=http://www.wilmott.com/blogs/paul/index.cfm/2008/4/29/Science-in-Finance-IX-In-defence-of-Black-Scholes-and-Merton |3=In defence of Black Scholes and Merton}}, [[Paul Wilmott]]
* {{Link||2=http://www.wilmott.com/blogs/paul/index.cfm/2008/7/23/Science-in-Finance-X-Dynamic-hedging-and-further-defence-of-BlackScholes |3=Dynamic hedging and further defence of Black-Scholes}}, [[Paul Wilmott]]
;Implementações computacionais
* Código fonte
** {{Link||2=http://www.espenhaug.com/black_scholes.html |3=Black–Scholes in Multiple Languages}}, espenhaug.com
** {{Link||2=http://www.global-derivatives.com/code/vba/BSEuro-Greeks.txt |3=VBA sourcecode for Black Scholes and Greeks}}, global-derivatives.com
** {{Link||2=http://www.optionpricing.org |3=Chicago Option Pricing Calculator}}, C#implementation, optionpricing.org
* Excel
** {{Link||2=http://www.optiontradingtips.com/pricing/free-spreadsheet.html |3=Option Pricing Spreadsheet with documented VBA}}, OptionTradingTips.com
** {{Link||2=http://www.quantnotes.com/softwaredata/excelvba/BSEuropeanCalculator.xls |3=Excel spreadsheet with VBA sourcecode}}, quantnotes.com
** {{Link||2=http://www.researchkitchen.co.uk/blog/archives/77 |3=Excel implementation and tutorial}}, researchkitchen.co.uk
** {{Link||2=http://www.quantonline.co.za/publications_and_research.html |3=Black&Scholes European option calculator including the Greeks}}, www.quantonline.co.za
** {{Link||2=http://www.global-derivatives.com/xls/European-CurrencyOption.xls |3=Foreign exchange option pricing}}, www.global-derivatives.com
* Real Time
** {{Link||2=http://www.optionstradedata.com/historical.html |3=End of day file with Implied Volatility}}, Options Trade Data
** {{Link||2=http://www.optionanimation.com |3=Black-Scholes tutorial based on graphic simulations}}, Jerry Marlow
** {{Link||2=http://cdmurray80.googlepages.com/optiongreeks |3=Surface Plots of Black-Scholes Greeks}}, Chris Murray
** {{Link||2=http://www.cba.ua.edu/~rpascala/revertGBM/BSOPMRForm.php |3=Real-time calculator of Call and Put Option prices when the underlying follows a Mean-Reverting Geometric Brownian Motion}}, [http://razecon.wordpress.com Razvan Pascalau]
** {{Link|pt|2=http://www.epx.com.br/ctb/bscalc.php |3=Black & Scholes calculator, with profitability of some operations}}, epx.com.br
* [http://jeremyganem.cluhost.info/2013/02/online-black-scholes-pricing/ Online Black-Scholes pricing]
;Históricos
* {{Link||2=http://www.pbs.org/wgbh/nova/stockmarket/ |3=Trillion Dollar Bet}}—Companion Web site to a Nova episode originally broadcast on February 8, 2000. ''"The film tells the fascinating story of the invention of the Black-Scholes Formula, a mathematical Holy Grail that forever altered the world of finance and earned its creators the 1997 Nobel Prize in Economics."''
* {{Link||2=http://www.bbc.co.uk/science/horizon/1999/midas.shtml |3=BBC Horizon}} A TV-programme on the so-called [[Midas formula]] and the bankruptcy of [[Long-Term Capital Management]] ([[LTCM]])
{{DEFAULTSORT:Black-Scholes}}
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