1. Financial Engineering Project Course

2. Lecture 2 Swaps Homework 2 More Java Fundamentals

3. Interest Rate Swaps Company A Company B 5.0% Source: John C. Hull LIBOR Rate

4. Interest Rate Swaps Company A Company B 5.0% Source: John C. Hull LIBOR Rate Suppose we have a three-year swap initiated on March 1, 1999, in which company B agrees to pay company A an interest rate of 5% per annum on notional principal of $100 million and in return company A agrees to pay company B the six-month LIBOR rate on the same notional principal.

5. Cash flow (in millions) to Company B in a $100 Million Three Year Interest Rate Swap when a fixed rate of 5% is paid and LIBOR is received DateLIBOR Floating Cash Flow received Fixed Cash Flow Paid Net Cash Flow 3/1/994.2% 9/1/994.8%+2.10-2.5-0.40 3/1/005.3%+2.40-2.5-0.10 9/1/005.5%+2.65-2.5+0.15 3/1/015.6%+2.75-2.5+0.25 9/1/015.9%+2.80-2.5+0.30 3/1/026.4%+2.95-2.5+0.45 Source: John Hull

6. Cash flow (in millions) to Company B in a $100 Million Three Year Interest Rate Swap when a fixed rate of 5% is paid and LIBOR is received DateLIBOR Floating Cash Flow received Fixed Cash Flow Paid Net Cash Flow 3/1/994.2% 9/1/994.8%+2.10-2.5-0.40 3/1/005.3%+2.40-2.5-0.10 9/1/005.5%+2.65-2.5+0.15 3/1/015.6%+2.75-2.5+0.25 9/1/015.9%+2.80-2.5+0.30 3/1/026.4%+2.95-2.5+0.45 Source: John Hull Six exchanges of payments Company B is always Paying the (5.0/2) % To its swap partner. $2.5 million

7. Cash flow (in millions) to Company B in a $100 Million Three Year Interest Rate Swap when a fixed rate of 5% is paid and LIBOR is received DateLIBOR Floating Cash Flow received Fixed Cash Flow Paid Net Cash Flow 3/1/994.2% 9/1/994.8%+2.10-2.5-0.40 3/1/005.3%+2.40-2.5-0.10 9/1/005.5%+2.65-2.5+0.15 3/1/015.6%+2.75-2.5+0.25 9/1/015.9%+2.80-2.5+0.30 3/1/026.4%+2.95-2.5+0.45 Source: John Hull The floating rate payments on the payment date are calculated using the six month LIBOR rate prevailing six months before the payment date.

8. Cash flow (in millions) to Company B in a $100 Million Three Year Interest Rate Swap when a fixed rate of 5% is paid and LIBOR is received DateLIBOR Floating Cash Flow received Fixed Cash Flow Paid Net Cash Flow 3/1/994.2% 9/1/994.8%+2.10-2.5-0.40 3/1/005.3%+2.40-2.5-0.10 9/1/005.5%+2.65-2.5+0.15 3/1/015.6%+2.75-2.5+0.25 9/1/015.9%+2.80-2.5+0.30 3/1/026.4%+2.95-2.5+0.45 Source: John Hull Company B pays Company A $(2.5 – 2.1) Million = $0.4 Million

9. Using the Swap to transform a liability Perhaps Company B would like to transform a floating rate loan to a fixed rate loan. Suppose that company B has arranged to borrow $100 Million at LIBOR plus 80 basis points. (1 basis point = one-hundredth of 1%) After entering into the swap, it has three sets of cash flows:

10. Using the Swap to transform a liability 1.It pays LIBOR plus 0.8% to its outside lenders. 2.It receives LIBOR under the terms of the swap. 3.It pays 5% under the terms of the swap. Post swap interest rate payment = 5.8% per annum (fixed)

11. Using the Swap to transform a liability For company A, the swap could have the effect of transforming a fixed-rate loan into a floating-rate loan. Suppose that company A has a three year $100 million loan outstanding on which it pays 5.2% per annum. After it has entered into the swap, it has three sets of cash flows:

12. Using the Swap to transform a liability 1.It pays 5.2% per annum to its outside lenders. 2.It pays LIBOR under the the terms of the swap. 3.It receives 5% per annum under the terms of the swap. This nets out to an interest rate payment of LIBOR + 0.2%. Or, LIBOR plus 20 basis points.

13. Using the Swap to transform a liability Company A Company B LIBOR 5% 5.2% LIBOR + 0.8%

14. Role of Financial Intermediary Company A Company B 5.2% LIBOR + 0.8% LIBOR 5.015% LIBOR 4.985% Financial Institution Source : John Hull

15. Homework 2 Class exercise Write an object-oriented program in Java that simulates the mechanics of an interest rate swap.