Your text is all grey, but adding a filter to my screen, I succeeded reading it !!
A possible answer is that your scheme is a finite difference explicit Euler scheme for which there exists a very famous known condition, called the CFL (Courant Friedrich Levy) condition.
In your particular scheme, I think that this condition could be something like (1 - sigma^2 S^2 Delta_t /Delta_s^2) >=0 . Taking Delta_S violating this condition leads to a consistent, but unstable, numerical scheme, which should explode accordingly to your observations.
To define an unconditionally stable numerical scheme, consider either a Crank Nicolson
, or fully implicit version.