Convex Regularization of Local Volatility Estimation in a Discrete Setting
29 Pages Posted: 11 Aug 2013 Last revised: 24 Feb 2016
Date Written: March 11, 2015
We apply convex regularization techniques to the problem of calibrating Dupire's local volatility surface model taking into account the practical requirement of discrete grids and noisy data.
Such requirements are the consequence of bid and ask spreads, quantization of the quoted prices and lack of liquidity of option prices for strikes far way from the at-the-money level.
We obtain convergence rates and results comparable to those obtained in the idealized continuous setting.
Our results allow us to take into account separately the uncertainties due to the price noise and those due to discretization errors. Thus allowing estimating better discretization levels both in the domain and in the image of the parameter to solution operator by a Morozov's discrepancy principle.
We illustrate the results with simulated as well as real market data. We also validate the results by comparing the implied volatility prices of market data with the computed prices of the calibrated model.
Keywords: Convex regularization, local volatility surfaces, regularization convergence rates, numerical methods for volatility calibration
JEL Classification: C61, C63, C80
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