  Prices of European call options in a regime-switching local volatility model
can be computed by solving a parabolic system which generalises 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.
