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

Mourad Bellassoued, Raymond Brummelhuis, Michel Cristofol () and Éric Soccorsi
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Raymond Brummelhuis: URCA - Université de Reims Champagne-Ardenne, LMR - Laboratoire de Mathématiques de Reims - URCA - Université de Reims Champagne-Ardenne - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Inverse problem; local-volatility; regime-switching model; stability inequality; parabolic Carleman inequality. (search for similar items in EconPapers)
Date: 2020
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Published in Mathematical Control and Related Fields, 2020, 10 (1), pp.189-215. ⟨10.3934/mcrf.2019036⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05318367

DOI: 10.3934/mcrf.2019036

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