COMPUTATION OF LOCAL VOLATILITIES FROM REGULARIZED DUPIRE EQUATIONS

Martin Hanke () and Elisabeth Rösler ()
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Martin Hanke: Fachbereich Mathematik, Johannes Gutenberg-Universität, 55099 Mainz, Germany
Elisabeth Rösler: Fachbereich Mathematik, Johannes Gutenberg-Universität, 55099 Mainz, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2005, vol. 08, issue 02, 207-221

Abstract: 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.

Keywords: Black–Scholes model; Dupire equation; local volatility; inverse problem; regularization; numerical differentiation (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (4)

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DOI: 10.1142/S0219024905002950

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