  In this paper, a geometric function is introduced to reflect the attenuation
speed of impact of one firm's default to its partner. If two firms are
competitions (copartners), the default intensity of one firm will decrease
(increase) abruptly when the other firm defaults. As time goes on, the impact
will decrease gradually until extinct. In this model, the joint distribution
and marginal distributions of default times are derived by employing the change
of measure, so can we value the fair swap premium of a CDS.
