Asymptotics and calibration of local volatility models
- 1 February 2002
- journal article
- Published by Taylor & Francis in Quantitative Finance
- Vol. 2 (1) , 61-69
- https://doi.org/10.1088/1469-7688/2/1/305
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.Keywords
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