Question: Question 4 [5 points]. Let To, - -- ,Tn denote an initial time T0 and a set of coupon payment dates. We write 61' =

Question 4 [5 points]. Let To, - -- ,Tn denote an initial time T0 and a set of coupon payment dates. We write 61' = TiTZ-_1 for i = 1, ..., n. An interest rate cap on LIBOR with strike K pays the holder 6i (L(E_1,E) K) if it is positive at T2- otherwise nothing for '12 = 1, ...,n. An interest rate floor pays the holder 6,; (K L(T_1, 11)) if it is positive at T1,, otherwise nothing for i : 1,71. 1. [2 point] Show that Vfap Vtoor : WSW\") where the cap, oor and swap are struck at K. 2. [3 point] Assume that notional is 1 and coupon is paid semi-annually (6i : 0.5). Consider it to be a 2-year swap (starting from T0 : t lasting until Tn : 15+ 2) and calculate a fair value of strike K. You may borrow the discount factors from the table in Question 2. Maturity T (years) Discount factor Z021? + T)

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