Spike T. Lee and
Hai-Wei Sun
10.4208/aamm.09-m09S06
Adv. Appl. Math. Mech., 1 (2009), pp. 845-861.
We consider pricing options in a jump-diffusion model which requires solving
a partial integro-differential equation. Discretizing the spatial direction
with a fourth order compact scheme leads to a linear system of ordinary
differential equations. For the temporal direction, we utilize the favorable
boundary value methods owing to their advantageous stability properties. In
addition, the resulting large sparse system can be solved rapidly by the
GMRES method with a circulant Strang-type preconditioner. Numerical results
demonstrate the high order accuracy of our scheme and the efficiency of the
preconditioned GMRES method.
