English, Article edition: COMPUTATION OF LOCAL VOLATILITIES FROM REGULARIZED DUPIRE EQUATIONS MARTIN HANKE; ELISABETH RÃSLER

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Physical Description
  • article
Language
  • English

Edition details

Title
  • COMPUTATION OF LOCAL VOLATILITIES FROM REGULARIZED DUPIRE EQUATIONS
Author
  • MARTIN HANKE
  • ELISABETH RÃSLER
Physical Description
  • article
Notes
  • We propose a new method to calibrate the local volatility function of an asset from observed option prices of the underlying. Our method is initialized with a preprocessing step in which the given data are smoothened using cubic splines before they are differentiated numerically. In a second step the Dupire equation is rewritten as a linear equation for a rational expression of the local volatility. This equation is solved with Tikhonov regularization, using some discrete gradient approximation as penalty term. We show that this procedure yields local volatilities which appear to be qualitatively correct.
  • BlackâScholes model, Dupire equation, local volatility, inverse problem, regularization, numerical differentiation
  • RePEc:wsi:ijtafx:v:08:y:2005:i:02:p:207-221
Language
  • English
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