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Convex Regularization of Local Volatility Estimation in a Discrete Setting

29 Pages Posted: 11 Aug 2013 Last revised: 24 Feb 2016

Vinicius Viana Luiz Albani

Computational Science Center - University of Vienna

Adriano De Cezaro

Federal University Foundation of Rio Grande (FURG)

Jorge P. Zubelli

Instituto de Matematica Pura e Aplicada (IMPA)

Date Written: March 11, 2015

Abstract

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

Suggested Citation

Albani, Vinicius Viana Luiz and De Cezaro, Adriano and Zubelli, Jorge P., Convex Regularization of Local Volatility Estimation in a Discrete Setting (March 11, 2015). Available at SSRN: https://ssrn.com/abstract=2308138 or http://dx.doi.org/10.2139/ssrn.2308138

Vinicius Viana Luiz Albani (Contact Author)

Computational Science Center - University of Vienna ( email )

Oskar Morgenstern-Platz 1
Vienna, Vienna 1090
Austria

Adriano De Cezaro

Federal University Foundation of Rio Grande (FURG) ( email )

Rio Grande, Rio Grande do Sul
Brazil

Jorge P. Zubelli

Instituto de Matematica Pura e Aplicada (IMPA) ( email )

Estrada Dona Castorina 110
Jardim Botanico
Rio de Janeiro, 22460
Brazil

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