2.2.3 Fair premium
We can now solve equation (2.2) for W * as a function of the
expected cumulative tranche loss E[M(t)]:
B(0, T ) E[M(T )] + f 0 T E[M(t)]dB(0, t)
W * = (
>m ) (2.3)
(K - K)(Tj - Tj-1) - f Tj
j=1 B(0, Tj) Tj-1 E[M(t)]dt
As soon as we can compute the expected tranche loss E[M(t)],
the calculation of the tranche fair premium becomes straightforward. In order
to do so, we then have to make further modelling assumptions on the behaviour
of the joint tranche loss distribution M(t), or equivalently L(t).
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