Don't stay local - extrapolation analytics for Dupire's local volatility

Details Don't stay local - extrapolation analytics for Dupire's local volatility Don't stay local - extrapolation analytics for Dupire's local volatility

2011-05-06

arxiv.org/abs/1105.1267v1

Economy

Quantitative Finance

Pricing of Securities

Scientific paper

A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied volatility surface; (ii) computation of the local volatility based on the resulting call price surface. Point (i), and in particular how to extrapolate the implied volatility in extreme strike regimes not seen in the market, has been the subject of numerous articles, starting with Lee (Math. Finance, 2004). In the present paper we give direct analytic insights into the asymptotic behavior of local volatility at extreme strikes.

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