On full calibration of hybrid local volatility and regime-switching models

Calibrating local regime-switching models is a challenging problem, especially when the volatility functions are assumed to depend on both of the underlying price and time. In this paper, the inverse problem of determining local volatility functions is firstly established and then solved through the Tikhonov regularization to obtain the optimal solution, which is achieved iteratively through a newly designed numerical algorithm. While our numerical tests with artificial data show that our algorithm can provide quite accurate and stable results, its performance with the involvement of real market data have been further demonstrated using options written on the S&P 500 index.