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

TL;DR

This paper proves Lipschitz stability for the inverse problem of reconstructing local volatilities in a regime-switching model from European call option prices, generalizing classical methods to a more complex setting.

Contribution

It establishes the first stability result for recovering local volatilities in a regime-switching local volatility model from market data.

Findings

Lipschitz stability of the inverse problem is proven.

Reconstruction of local volatilities is stable under data perturbations.

The approach extends classical Black-Scholes methods to regime-switching models.

Abstract

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.