Editing Black–Scholes model (section)

== History ==
[[Louis Bachelier|Louis Bachelier's]] thesis<ref>{{Cite book |last=Bachelier |first=Louis |url=http://www.radio.goldseek.com/bachelier-thesis-theory-of-speculation-en.pdf |title=Théorie de la Spéculation |date=1900 |publisher=Annales Scientifiques de l'École Normale Supérieure |year=1900 |edition=Series 3, 17 |location=France |publication-date=2011 |pages=21-86 |language=French |translator-last=May |trans-title=Theory of Speculation}}</ref> in 1900 was the earliest publication to apply Brownian motion to derivative pricing, though his work had little impact for many years and included important limitations for its application to modern markets.<ref>{{Cite web |last=Houstecky |first=Petr |title=Black-Scholes Model History and Key Papers |url=https://www.macroption.com/black-scholes-history/#ref-4 |url-status=live |archive-url=https://web.archive.org/web/20240614192845/https://www.macroption.com/black-scholes-history/ |archive-date=Jun 14, 2024 |access-date=Oct 3, 2024 |website=Macroption}}</ref> In the 1960's [[Case Sprenkle]],<ref>{{Cite journal |last=Sprenkle |first=C. M. |date=1961 |title=Warrant prices as indicators of expectations and preferences. |journal=Yale Economic Essays |volume=1 |issue=2 |pages=178-231}}</ref> James Boness,<ref>{{Cite journal |last=Boness |first=James |date=1964 |title=Elements of a Theory of Stock-Option Value |url=https://www.journals.uchicago.edu/doi/abs/10.1086/258885 |journal=Journal of Political Economy |volume=72 |issue=2 |pages=163-175 |via=University of Chicago Press}}</ref> [[Paul Samuelson]],<ref>{{Cite journal |last=Samuelson |first=Paul |date=1965 |title=Rational Theory of Warrant Pricing |url=https://www.proquest.com/docview/214192591?sourcetype=Scholarly%20Journals |journal=Industrial Management Review |volume=6 |issue=2 |pages=13-31 |via=ProQuest}}</ref> and Samuelson's Ph.D. student at the time [[Robert C. Merton]]<ref>{{Cite journal |last=Samuelson |first=Paul |last2=Merton |first2=Robert |date=1969 |title=A Complete Model of Warrant Pricing that Maximizes Utility |url=https://www.proquest.com/docview/214192177?pq-origsite=gscholar&fromopenview=true&sourcetype=Scholarly%20Journals |journal=Industrial Management Review |volume=10 |issue=2 |pages=17-46 |via=ProQuest}}</ref> all made important improvements to the theory of options pricing. 

[[Fischer Black]] and [[Myron Scholes]] demonstrated in 1968 that a dynamic revision of a portfolio removes the [[expected return]] of the security, thus inventing the ''risk neutral argument''.<ref>Taleb, 1997. pp. 91 and 110–111.</ref><ref>Mandelbrot & Hudson, 2006. pp. 9–10.</ref> They based their thinking on work previously done by market researchers and practitioners including the work mentioned above, as well as work by [[Sheen Kassouf]] and [[Edward O. Thorp]]. Black and Scholes then attempted to apply the formula to the markets, but incurred financial losses, due to a lack of [[risk management]] in their trades. In 1970, they decided to return to the academic environment.<ref>Mandelbrot & Hudson, 2006. p. 74</ref> After three years of efforts, the formula—named in honor of them for making it public—was finally published in 1973 in an article titled "The Pricing of Options and Corporate Liabilities", in the ''[[Journal of Political Economy]]''.<ref>Mandelbrot & Hudson, 2006. pp. 72–75.</ref><ref>Derman, 2004. pp. 143–147.</ref><ref>Thorp, 2017. pp. 183–189.</ref> [[Robert C. Merton]] was the first to publish a paper expanding the mathematical understanding of the options pricing model, and coined the term "Black–Scholes [[options pricing]] model".

The formula led to a boom in options trading and provided mathematical legitimacy to the activities of the [[Chicago Board Options Exchange]] and other options markets around the world.<ref name="mackenzie">{{cite book|title= An Engine, Not a Camera: How Financial Models Shape Markets|last= MacKenzie|first= Donald|author-link= Donald Angus MacKenzie|year= 2006|publisher= MIT Press|location= Cambridge, MA|isbn= 0-262-13460-8|url= https://archive.org/details/enginenotcamerah00mack_0}}</ref>

Merton and Scholes received the 1997 [[Nobel Memorial Prize in Economic Sciences]] for their work, the committee citing their discovery of the risk neutral dynamic revision as a breakthrough that separates the option from the risk of the underlying security.<ref>{{Cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1997/press.html|title = The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1997}}</ref> Although ineligible for the prize because of his death in 1995, Black was mentioned as a contributor by the [[Swedish Academy of Science|Swedish Academy]].<ref>{{cite press release|url=http://nobelprize.org/nobel_prizes/economics/laureates/1997/press.html|title=Nobel Prize Foundation, 1997 |access-date=March 26, 2012|date=October 14, 1997}}</ref>