Numerical Identification of Time-Dependent Volatility in European Options with Two-Stage Regime-Switching

We develop numerical algorithms to solve inverse problems of determining time-dependent volatility according to point measurements inside of a truncated domain for regime-switching models of European options. An average linearization in time of the diffusion terms of the initial-boundary problems is used. Difference schemes on Tavella-Randall grids are derived. The numerical method is based on a decomposition of the difference solution with respect to the volatility for which the transition to the new time layer is carried out by solving two discrete elliptic system problems. Numerical experiments are performed to verify the effectiveness and robustness of the new algorithms.

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