TY - JOUR
T1 - Fourth Order Compact Boundary Value Method for Option Pricing with Jumps
AU - Lee , Spike T.
AU - Sun , Hai-Wei
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 845
EP - 861
PY - 2009
DA - 2009/01
SN - 1
DO - http://doi.org/10.4208/aamm.09-m09S06
UR - https://global-sci.org/intro/article_detail/aamm/8401.html
KW - Partial integro-differential equation, fourth order compact scheme, boundary
value method, preconditioning, Toeplitz matrix.
AB - <p style="text-align: justify;">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.</p>