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Calibration of Volatility: Coupling between alternative regularization strategy and Dupire’s Equation

R. Aboulaich, I. Medarhri

Abstract


We propose in this work a Tikhonov regularization method for a calibration problem. The goal is to identify the local volatility from some observed option prices on the market. The proposed method, is used by N.ElHassan (Chiarella, Craddock and El-Hassan, 2007) and Lagnado and Osher (Lagnado and Osher, 1997) using a Black-Scholes model, in this paper
we propose to use Dupire model coupled with the optimization algorithms proposed in (Chiarella et al., 2007) and (Lagnado and Osher, 1997). In order to improve the approximation of the initial guess of the volatility we propose to use a statistical approximation. The obtained results are compared with those obtained by N.El Hassan and with Lamarti (Aboulaich and Lamarti, 2013) which proposes another algorithm named ”jump indicator” in the case of a discontinuous volatility.

Keywords


Inverse problem, Locale volatility, Black-Scholes formula, Dupire Formula, Optimization, Tikhonov regularization.

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