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On full calibration of hybrid local volatility and regime‐switching models
Author(s) -
He XinJiang,
Zhu SongPing
Publication year - 2018
Publication title -
journal of futures markets
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.88
H-Index - 55
eISSN - 1096-9934
pISSN - 0270-7314
DOI - 10.1002/fut.21901
Subject(s) - local volatility , tikhonov regularization , volatility (finance) , regularization (linguistics) , econometrics , inverse , computer science , mathematical optimization , implied volatility , economics , inverse problem , mathematics , mathematical analysis , artificial intelligence , geometry
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.