Before revision:  In particular, the performance of cubic and quintic Hermite and cubic spline interpolation is explored in estimating the coupled asset, delta, gamma  and speed options in the set of equations. The numerical method is finally tested with several examples.
After revision:  In particular, the performance of cubic and quintic Hermite and cubic spline interpolation is explored in estimating the coupled asset, delta, gamma and speed options in the present regime is estimated based on Hermite interpolations. Finally, the numerical method is finally tested with several examples.