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Black-Scholes: En prissättningsmodell för optioner
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2010 (Swedish)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This paper aims to derive the Black-Scholes equation for readers without advanced knowledge in finance and mathematics. To succeed, this paper contains a theoretical chapter in which concepts such as options, interest rate, differential equations and stochastic variable are explained. This paper also presents the theory of stochastic processes such as the Wiener process and Ito process. In the chapter on the Black-Scholes model the Ito process is used to describe price of shares and with the help of Ito's lemma Black-Scholes equation can be derived. In the paper, assumptions are listed that apply to the Black-Scholes model and then uses the Black-Scholes equation to calculate the price of a European call option. Finally, exotic options are described and also how options can be used to reduce risks.

Abstract [sv]

Uppsatsens mål är att härleda Black-Scholes ekvation för läsare utan avancerade kunskaper inom finansiering och matematik. För att lyckas med detta innehåller uppsatsen ett teorikapitel där begrepp så som optioner, ränta, differentialekvation och stokastisk variabel förklaras. Där presenteras även teorier för stokastiska processer så som Wienerprocessen och Itoprocessen. I kapitlet om Black-Scholes modell används Itoprocessen för att beskriva aktiepriset och med hjälp av Itos lemma härleds Black-Scholes ekvation. Uppsatsen ställer upp antaganden som gäller för Black-Scholes modell och använder sedan Black-Scholes ekvation för att beräkna priset på en europeisk köpoption. Avslutningsvis beskrivs exotiska optioner samt hur optioner kan användas för att reducera risker.

Place, publisher, year, edition, pages
2010. , 31 p.
Keyword [sv]
Black Scholes, optioner
National Category
URN: urn:nbn:se:umu:diva-35084OAI: diva2:328937
Physics, Chemistry, Mathematics
Available from: 2010-09-02 Created: 2010-07-06 Last updated: 2010-09-02Bibliographically approved

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