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Pricing American and European options under the binomial tree model and its Black-Scholes limit model
Linnaeus University, Faculty of Technology, Department of Mathematics.
2017 (English)Independent thesis Basic level (degree of Bachelor), 180 HE creditsStudent thesis
Abstract [en]

We consider the N step binomial tree model of stocks. Call options and put options of European and American type are computed explicitly. With appropriate scaling in time and jumps,  convergence of the stock prices and the option prices are obtained as N-> infinite. The obtained convergence is the Black-Scholes model and, for the particular case of European call option, the Black-Scholes formula is obtained. Furthermore, the Black-Scholes partial differential equation is obtained as a limit from the N step binomial tree model. Pricing of American put option under the Black-Scholes model is obtained as a limit from the N step binomial tree model.

With this thesis, option pricing under the Black-Scholes model is achieved not by advanced stochastic analysis but by elementary, easily understandable probability computation. Results which in elementary books on finance are mentioned briefly are here derived in more details.

Some important Java codes for N step binomial tree option prices are constructed by the author of the thesis.

Place, publisher, year, edition, pages
2017. , p. 64
Keywords [en]
European option, American option, Binomial tree model, Black-Scholes PDE, Black-Scholes option pricing formula
National Category
Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-68264OAI: oai:DiVA.org:lnu-68264DiVA, id: diva2:1147763
Subject / course
Mathematics
Educational program
Applied Mahtematics Programme, 180 credits
Presentation
2017-09-28, B2034, B building, vaxjo linnaeus university, 18:49 (English)
Supervisors
Examiners
Available from: 2017-10-09 Created: 2017-10-08 Last updated: 2017-10-09Bibliographically approved

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Pricing American and European options under the binomial tree model and its Black-Scholes limit model(1280 kB)437 downloads
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf