# Asymptotics and calibration of local volatility models

@article{Berestycki2002AsymptoticsAC, title={Asymptotics and calibration of local volatility models}, author={Henri Berestycki and J{\'e}r{\^o}me Busca and Igor Florent}, journal={Quantitative Finance}, year={2002}, volume={2}, pages={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.

## 192 Citations

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