Stable reconstruction of the volatility in a regime-switching local-volatility model

Bellassoued Mourad; Brummelhuis Raymond; Cristofol Michel; Soccorsi Éric

doi:10.3934/mcrf.2019036

Article Contents

2020, Volume 10, Issue 1: 189-215. Doi: 10.3934/mcrf.2019036

This issue Previous Article A direct method based on the Clenshaw-Curtis formula for fractional optimal control problems Next Article

Stable reconstruction of the volatility in a regime-switching local-volatility model

1.
University of Tunis El Manar, National Engineering School of Tunis, ENIT-LAMSIN, B.P. 37, 1002 Tunis, Tunisia
2.
Laboratoire de Mathématiques de Reims, Université de Reims, EA 4535, France
3.
Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
4.
Aix-Marseille Univ, Université de Toulon, CNRS, CPT, Marseille, France

^* Corresponding author: eric.soccorsi@univ-amu.fr
^* Corresponding author: eric.soccorsi@univ-amu.fr

Received: November 30, 2017

Revised: March 31, 2019

Early access: August 2019

Published: February 2020

The last author is partially supported by the Agence Nationale de la Recherche under grant ANR-17- CE40-0029

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Abstract

Prices of European call options in a regime-switching local-volatility model can be computed by solving a parabolic system which generalizes the classical Black and Scholes equation, giving these prices as functionals of the local-volatilities. We prove Lipschitz stability for the inverse problem of determining the local-volatilities from quoted call option prices for a range of strikes, if the calls are indexed by the different states of the continuous Markov chain which governs the regime switches.

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Mathematics Subject Classification: Primary: 35R30, 35K10; Secondary: 58J35.

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References

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