Asymptotics and calibration of local volatility models

H. Berestycki, J. Busca and I. Florent

Quantitative Finance, 2002, vol. 2, issue 1, 61-69

Abstract: We derive a direct link between local and implied volatilities in the form of a quasilinear degenerate parabolic partial differential equation. Using this equation we establish closed-form asymptotic formulae for the implied volatility near expiry as well as for deep in- and out-of-the-money options. This in turn leads us to propose a new formulation near expiry of the calibration problem for the local volatility model, which we show to be well posed.

Date: 2002
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Citations: View citations in EconPapers (58)

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DOI: 10.1088/1469-7688/2/1/305

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