e are seeking static replication of the
function
with a linear combination of the functions
defined in the previous section. Using the results
(
Recovery of implied
distribution
) we
write
for some number
.
We perform integration by parts to move the derivatives to the function
:
To simplify the boundary terms we derive the put-call parity for function
and
:
where the
is the forward price of
.
We also note that we separated the values of
and use the out-of-money contracts so that the extreme boundary terms would
vanish. We simplify the boundary terms as
follows: