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Challenges with Using the Black-Scholes Model for Pricing Long-Maturity Options
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2024 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

This thesis investigates the application of the Black-Scholes model for pricing long-maturity options, primarily utilizing historical data on S\&P500 options. It compares prices computed with the Black-Scholes formula to actual market prices and critically examines the validity of the Black-Scholes model assumptions over long time frames. The assumptions mainly focused on are the constant volatility assumption, the assumption of normally distributed returns, the constant interest rate assumption and the no transaction cost assumption. The results show that the differences between computed prices and actual prices decrease as options get closer to maturity. They also show that several of the Black-Scholes model assumptions are not entirely realistic over long time frames. The conclusion of the thesis is that there are several limitations to the Black-Scholes model when it comes to pricing long-maturity options.

Place, publisher, year, edition, pages
2024.
Series
TRITA-SCI-GRU ; 2024:159
Keywords [en]
Black-Scholes, option pricing, long-maturity options, S\&P500, implied volatility, financial model assumptions
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-349254OAI: oai:DiVA.org:kth-349254DiVA, id: diva2:1880210
Educational program
Master of Science in Engineering -Engineering Physics
Supervisors
Examiners
Available from: 2024-07-01 Created: 2024-07-01 Last updated: 2024-07-01Bibliographically approved

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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • 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