Resumen
In this paper, we recover the European option volatility function σ(t)" role="presentation">??(??)s(t)
s
(
t
)
of the underlying asset and the fractional order α" role="presentation" style="position: relative;">??a
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of the time fractional derivatives under the time fractional Vasicek model. To address the ill-posed nature of the inverse problem, we employ Tikhonov regularization. The Alternating Direction Multiplier Method (ADMM) is utilized for the simultaneous recovery of the parameter α" role="presentation" style="position: relative;">??a
a
and the volatility function σ(t)" role="presentation" style="position: relative;">??(??)s(t)
s
(
t
)
. In addition, the existence of a solution to the minimization problem has been demonstrated. Finally, the effectiveness of the proposed approach is verified through numerical simulation and empirical analysis.