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Rational Shapes of the Local Volatility Surface

Please always quote using this URN:urn:nbn:de:0296-matheon-11519
  • A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. In the present note we provide new analytic insights into the asymptotic behavior of local volatility in the wings. We present a general approximation formula and specialize it to the Heston model, showing that local variance is linear in the wings. This further justifies the choice of certain local volatility parametrizations.

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Metadaten
Author:Stefano De Marco
URN:urn:nbn:de:0296-matheon-11519
Referee:Peter Karl Friz
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2012/07/17
Release Date:2012/07/17
Tag:Asymptotic methods in Finance; local volatility; option pricing; saddle-point method
Institute:Technische Universität Berlin
MSC-Classification:60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H10 Stochastic ordinary differential equations [See also 34F05]
60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Hxx Stochastic analysis [See also 58J65] / 60H35 Computational methods for stochastic equations [See also 65C30]
Preprint Number:970
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