1. Pricing the roller coaster SWAP contract - 30 points Today is 31st-Jan-2002. Consider a 10-year roller coaster SWAP. The floating leg is indexed to the 6-month T-bill. The fixed leg payment is annually. A real estate con- struction company wants to enter into this roller coaster SWAP contract by receiving the floating leg and pays the fixed leg. The notional amount on the fixed leg is $50 million dollars. However, the notional amount on the floating leg will vary seasonally through the 10-year period. During the summer time, the company expects to depend on a large cash flow. Therefore the notional amount on the floating leg for the summer is three times the size of the notional contract for the winter. Make any other assump- tions, if necessary. However, use your common sense. Unreasonable assumptions will not be accepted. Zero-rates data are available on FRED II or GSW websites. You need to extrapolate or estimate the term structure first. (a) Assume that the fixed annual leg payment is 5% and that this roller coaster SWAP contract is traded at par. What is the notional amount on the floating leg of this SWAP contract for the summer? (b) If the notional amount on the floating leg for the summer is $25 million, what is the rate for the fixed leg payment? Assume that this roller coaster SWAP contract is traded at par. (c) Let's assume that you have entered into this SWAP contract and the fixed leg payment rate is 5% (i.e. from part a). Recall that today is 31st-Jan-2002 and this SWAP contract is traded at par. Now, a year has gone by and the date is 31st-Jan-2003. What is the price of this roller SWAP contract?