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Valuation of portfolios under uncertain volatility: Black-Scholes-Barenblatt equations and the static hedging
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE).
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE).
2007 (English)Independent thesis Advanced level (degree of Master (One Year))Student thesis
Abstract [en]

The famous Black-Scholes (BS) model used in the option pricing theory

contains two parameters - a volatility and an interest rate. Both

parameters should be determined before the price evaluation procedure

starts. Usually one use the historical data to guess the value of these

parameters. For short lifetime options the interest rate can be estimated

in proper way, but the volatility estimation is, as well in this case,

more demanding. It turns out that the volatility should be considered

as a function of the asset prices and time to make the valuation self

consistent. One of the approaches to this problem is the method of

uncertain volatility and the static hedging. In this case the envelopes

for the maximal and minimal estimated option price will be introduced.

The envelopes will be described by the Black - Scholes - Barenblatt

(BSB) equations. The existence of the upper and lower bounds for the

option price makes it possible to develop the worse and the best cases

scenario for the given portfolio. These estimations will be financially

relevant if the upper and lower envelopes lie relatively narrow to each

other. One of the ideas to converge envelopes to an unknown solution

is the possibility to introduce an optimal static hedged portfolio.

Place, publisher, year, edition, pages
Högskolan i Halmstad/Sektionen för Informationsvetenskap, Data- och Elektroteknik (IDE) , 2007.
Keyword [en]
volatility, Black-Scholes-Barenbladt, finite differences method
Identifiers
URN: urn:nbn:se:hh:diva-1634Local ID: 2082/2015OAI: oai:DiVA.org:hh-1634DiVA: diva2:238852
Presentation
(English)
Uppsok
Physics, Chemistry, Mathematics
Available from: 2008-06-25 Created: 2008-06-25 Last updated: 2009-10-26

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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