CONVEX REGULARIZATION OF LOCAL VOLATILITY ESTIMATION

Vinicius Albani (), Adriano de Cezaro () and Jorge P. Zubelli
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Vinicius Albani: Department of Mathematics, Federal University of Santa Catarina, Trindade, Florianopolis, Santa Catarina 88.040-900, Brazil
Adriano de Cezaro: Institute of Mathematics, Statistics and Physics, Federal University of Rio Grande, Av. Italia Km 8, Rio Grande, Rio Grande do Sul 96201-900, Brazil
Jorge P. Zubelli: Instituto of Pure and Applied Mathematics, Estrada Dona Castorina, 110, Jardim Botnico, Rio de Janeiro, Rio de Janeiro 22460-320, Brazil

International Journal of Theoretical and Applied Finance (IJTAF), 2017, vol. 20, issue 01, 1-37

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 away 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 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1142/S0219024917500066

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