Power options II
A capped power call is a K1-strike power call whose payout is capped at K2 > K1, that is, it has payout at time T
Capped power calls were briefly popular in derivative markets in the mid-1990s.
(a) Write down (but do not solve) the integral expression for the price of the capped power call.
(b) Suppose K1 = 100 and K2 = 115, and that you observe call option prices for K = 100, 105, 110 and 115. By comparing the payout functions of the capped power call with linear combinations of calls, find upper and lower bounds for the price of the capped power call in terms of the four call prices. Is there a least expensive upper bound and a most expensive lower bound? If so, find them.