  In this paper, a multidimensional system of parabolic partial differential
equations arising in European option pricing under a regime-switching market
model is studied in details. For solving that numerically, one must truncate
the domain and impose an artificial boundary data. By deriving an estimate of
the domain truncation error at all the points in the truncated domain, we
extend some results in the literature those deal with option pricing equation
under constant regime case only. We differ from the existing approach to obtain
the error estimate that is sharper in certain region of the domain. Hence, the
minimum of proposed and existing gives a strictly sharper estimate. A
comprehensive comparison with the existing literature is carried out by
considering some numerical examples. Those examples confirm that the
improvement in the error estimates is significant.
