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On Tikhonov regularization method in calibration of volatility term-structure |
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PP: 93-100 |
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Author(s) |
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Ahmad Reza Yazdanian,
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Abstract |
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| In this paper, we consider inverse problem arising in calibration of time-dependent volatility function
from the Black-Scholes model and analyze its ill-posedness phenomena. The forward operator of the
inverse problem under some consideration decomposes into an inner linear convolution operator and
an outer nonlinear Nemytskii operator given by a Black-Scholes function. Using Chebyshev collocation
method, we transfer the inner linear operator to a linear system. Since the resulting matrix equation
is badly ill-conditioned, a regularized solution is obtained by employing the Tikhonov regularization
method, while the choice of the regularization parameter are based on generalized cross-validation(GCV)
and L-curve criterions. Numerical case studies illustrate the eciency and accuracy of the presented
method. |
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