Description:
In this paper, we consider the inverse problem of calibrating a generalization of the bivariate Ornstein-Uhlenbeck model introduced by Lo and Wang. Even
though the generalized Black-Scholes option pricing formula still holds, option prices change in comparison to the classical Black-Scholes model. The time-dependent
volatility function and the other (real-valued) parameters in the model are calibrated simultaneously from option price data and from some empirical moments of
the logarithmic returns. This gives an ill-posed inverse problem, which requires a
regularization approach. Applying the theory of Engl, Hanke and Neubauer concerning Tikhonov regularization we show convergence of the regularized solution
to the true data and study the form of source conditions which ensure convergence
rates.