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

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

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  • 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.

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


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