4. Interest rate options a) Show that a 5-year floating-rate note with a floor that pays off max(LIBOR_(t-1), 5%) each year using 1-year LIBOR, plus repayment of face value at maturity, is equivalent to a floating-rate note plus a portfolio of put options on LIBOR. b) Show that the above floating-rate note is also equivalent to a straight bond plus a portfolio of call options on LIBOR. c) Show that a 5-year floating-rate note with a ceiling that pays off min(LIBOR_(t-1), 5%) each year is equivalent to a floating-rate note minus a portfolio of call options on LIBOR.