The spot price of IBM is $100.
The risk-free rate is 3%
.Consider the eight barrier versions of the 1-year IBM European call with strike price $110 and barrier $120. Denote their prices today by c_do, c_di, c_uo,c_ui, p_do, p_di, p_uo, _pui, where for example c_do is the down-and-out call while p_ui is the up-and-in put.
(a) List all of the options whose price today is 0
(b) Suppose that cuo = 3, pui = 4, puo = 2. Compute the price of a portfolio which is long 7 up-and-in calls and short 5 up-and-out puts