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The SABR Model: Calibrated for Swaption's Volatility Smile
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
2014 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
SABR Modellen : Kalibrerad för Swaptioner med Volatilitetsleende (English)
Abstract [en]

Problem: The standard Black-Scholes framework cannot incorporate the volatility smiles usually observed in the markets. Instead, one must consider alternative stochastic volatility models such as the SABR. Little research about the suitability of the SABR model for Swedish market (swaption) data has been found.

Purpose: The purpose of this paper is to account for and to calibrate the SABR model for swaptions trading on the Swedish market. We intend to alter the calibration techniques and parameter values to examine which method is the most consistent with the market.

Method: In MATLAB, we investigate the model using two different minimization techniques to estimate the model’s parameters. For both techniques, we also implement refinements of the original SABR model.

Results and Conclusion: The quality of the fit relies heavily on the underlying data. For the data used, we find superior fit for many different swaption smiles. In addition, little discrepancy in the quality of the fit between methods employed is found. We conclude that estimating the α parameter from at-the-money volatility produces slightly smaller errors than using minimization techniques to estimate all parameters. Using refinement techniques marginally increase the quality of the fit.

Place, publisher, year, edition, pages
2014. , 68 p.
Keyword [en]
SABR, Volatility smile, Swaption, Stochastic volatility, Black-Scholes model
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-24627OAI: oai:DiVA.org:mdh-24627DiVA: diva2:704410
Subject / course
Mathematics/Applied Mathematics
Presentation
2014-02-28, Västerås, 17:15 (English)
Supervisors
Examiners
Available from: 2014-03-12 Created: 2014-03-12 Last updated: 2014-03-12Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
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  • de-DE
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