Local volatility calibration using an adjoint proxy

Gabriel Turinici (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We document the calibration of the local volatility in a frame- work similar to Coleman, Li and Verma. The quality of a surface is assessed through a functional to be optimized; the specificity of the approach is to separate the optimization (performed with any suitable optimization algorithm) from the computation of the functional where we use an adjoint (as in L. Jiang et. al.) to obtain an approximation; moreover our main calibration variable is the implied volatility (the procedure can also accommodate the Greeks). The procedure per- forms well on benchmarks from the literature and on FOREX data.

Mots clés: calibration; local volatility; implied volatility; Dupire formula; adjoint

Domaines: Economies et finances; Analyse numérique [math.NA]

Gabriel Turinici. Local volatility calibration using an adjoint proxy. 2008. ⟨hal-00306187v1⟩