- inner loop: identification of the time dependent drift function by solving the regularized curve fitting problem given the speed and the volatility parameters
- outer loop: identification of the speed and volatility parameter, such that the model prices of caps and swaptions are close to the quoted market prices.
Formulation as a minimization problem including a penalty term (penalizing the L2 norm or the H1 norm of the solution x), leads to a smooth drift, which is consistent with the initial term structure of interest.
For the calculations in step 2 of the algorithm we minimize the functional
To end up with a calibration algorithm which is not too time consuming (compared to models where analytic formulas are available), for the calculation of the gradient with respect to the time dependent drift parameter an adjoint approach is applied.
Finally we end up with a calibration algorithm with a computational time < 10 sec.
Goodness of Fit