2. What follows is the description of a rather complex swap structured by a bank. The structure is sold for the purpose of liability management and involves an exotic option (digital cap) and a CMS component. At time 0 the bank and the client agree to exchange cash flows semiannually for 5 years according to the following rules: • The bank pays semiannually, 6m-Libor on the notional amount. This is a vanilla swap. • The client pays a coupon ct according to the following formula: ct = c1t−c2t (45) where c1t = ⎧ ⎨ ⎩ Libor + 47 bp% if Libor < 4.85% 5.23% if 4.85% < Libor < 6.13% 2.98% if Libor > 6.13% c2t = { cms (30Y ) − (cms (10Y ) + 198 bp)} for the first two years. And c2t = 8{cms (30Y ) − (cms (10Y ) + 198 bp)} for the last three years.

(a) Unbundle this Libor exotic into vanilla products the best you can.

(b) Why would an investor demand this product? What would be his or her expectations?