4. Spot-Rate Options Caps and floors have become a mainstay of corporate funding strate- 100+2 gies. Recently hired to expand the sales of a struggling fixed income group at a minor Wall Street investment bank you embark upon an ambitious strategy to introduce your customers, primarily small- and medium-sized enterprises (SMEs), to caps and floors. Unfortunately, you face a lot of hostility from some old-fashioned elements among your clients' senior manage- ment. In order to assuage their fears you decide to fully document all transactions involving 5 spot-rate options which shows that they are straightforward generalizations of options on securities. Please note that this problem involves a fair amount of research and thought. A good starting point might be the textbook and other online resources. Fortunately, you also remember some materials from your fixed-income course in college and, especially, a technical note written by your old professor. (a) First you need to carefully define the two instruments. What is a cap? What is a floor? (b) An important customer has asked you for quotes on a cap and a floor. Calling up the relevant information on you firm's intranet, it displays the current pricing model in the form of the following two-period binomial lattice (t = 0,1,2) for the one-year LIBOR rate with yearly step size At = 1: t = 0 t = 1 t = 2 Tuu = 6.6150 Tu = 6.3000 To = 6.000 Tud = 6.0000 rd = 5.7143 rdd = 5.4421 What does it mean to price an at-the-money European option? Using the preceding lattice and risk-neutral probabilities of q = 1 = 1 - 9 you now calculate the price of an at-the-money European caplet (call) on the 1Y LIBOR rate expiring in one year's time at t 1. Similarly, you derive the price of an at-the-money European floorlet (put) on the 1Y LIBOR rate expiring in one year's time at t = 1. (c) How do issuers and investors use caps and floors? Explain. (d) Optional. Finally, you contemplate the recent sale of a 12/24 FRA. How would you use LIBOR options to limit your bank's interest-rate exposure on this transaction?