umu.sePublications
Change search
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
Volatility and variance swaps: A comparison of quantitative models to calculate the fair volatility and variance strike
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2017 (English)Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
Abstract [en]

Volatility is a common risk measure in the field of finance that describes the magnitude of an asset’s up and down movement. From only being a risk measure, volatility has become an asset class of its own and volatility derivatives enable traders to get an isolated exposure to an asset’s volatility. Two kinds of volatility derivatives are volatility swaps and variance swaps.

The problem with volatility swaps and variance swaps is that they require estimations of the future variance and volatility, which are used as the strike price for a contract. This thesis will manage that difficulty and estimate strike prices with several different models. I will de- scribe how the variance strike for a variance swap can be estimated with a theoretical replicating scheme and how the result can be manipulated to obtain the volatility strike, which is a tech- nique that require Laplace transformations. The famous Black-Scholes model is described and how it can be used to estimate a volatility strike for volatility swaps. A new model that uses the Greeks vanna and vomma is described and put to the test. The thesis will also cover a couple of stochastic volatility models, Exponentially Weighted Moving Average (EWMA) and Gener- alized Autoregressive Conditional Heteroskedasticity (GARCH).

The models’ estimations are compared to the realized volatility. A comparison of the mod- els’ performance over 2015 is made as well as a more extensive backtesting for Black-Scholes, EWMA and GARCH.

The GARCH model performs the best in the comparison and the model that uses vanna and vomma gives a good result. However, because of limited data, one can not fully conclude that the model that uses vanna and vomma can be used when calculating the fair volatility strike for a volatility swap. 

Place, publisher, year, edition, pages
2017. , 42 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:umu:diva-135910OAI: oai:DiVA.org:umu-135910DiVA: diva2:1107407
Educational program
Master of Science in Engineering and Management
Supervisors
Examiners
Available from: 2017-06-13 Created: 2017-06-09 Last updated: 2017-06-13Bibliographically approved

Open Access in DiVA

fulltext(1309 kB)31 downloads
File information
File name FULLTEXT01.pdfFile size 1309 kBChecksum SHA-512
48e33fee149ce25b7a312dddda7ce83c134d9d66ff02131cbbfe8363577c1701f451549c6b0f7a6faa1e6e3c2aa756fa9edde18fda28c3acff5c63f12aa46df6
Type fulltextMimetype application/pdf

By organisation
Department of Mathematics and Mathematical Statistics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 31 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 59 hits
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