A general framework is developed to treat optimal control problems for
a generalized Black-Scholes model, which is used for option pricing.
The volatility function is retrieved from a set of market observations.
The optimal volatility function is found by minimizing the cost functional
measuring the discrepancy between the model solution (pricing) and the
observed market price, via the unconstrained minimization algorithm of
the quasi-Newton limited memory type. The gradient is computed via the adjoint method.
The effectiveness of the method is demonstrated on an European call