Calibration of local volatility using the local and implied instantaneous variance
Résumé
We document the calibration of the local volatility through a functional to be optimized; our calibration variables are the local and implied instantaneous variances whose theoretical properties are fully explored within a particular class of volatilities. We confirm the theoretical results through a numerical procedure where we separate the parametric optimization (performed with any suitable optimization algorithm) from the computation of the functional by the use of an adjoint to obtain an approximation. The procedure performs well on benchmarks from the literature and on FOREX data.
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