Lecture08[1]

# Lecture08[1] - STAT 2820 Chapter 8 Interest Rate Swaps by...

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Unformatted text preview: STAT 2820 Chapter 8 Interest Rate Swaps by K.C. Cheung 8.1 Interest rate swap 8.1.1 Suppose that ABC has an n-year \$ A floating-rate debt, so that at the end of the i-th year ( i = 1 , 2 ,...,n ), the interest payment of ABC is \$ A · r ( i- 1 ,i ). The rate r ( i- 1 ,i ) is floating and is only known at time i- 1, the beginning of the year. In other words, the future interest payments of ABC are uncertain at time 0: Time Interest Payment Principal paid 1 Ar (0 , 1), as the interest for the first year 2 Ar (1 , 2), as the interest for the second year . . . . . . n- 1 Ar ( n- 2 ,n- 1), as the interest for the ( n- 1)-th year n Ar ( n- 1 ,n ), as the interest for the n-th year A Note that r (1 , 2), r (2 , 3), ..., r ( n- 1 ,n ) are 1-year rates in the future, which are unknown at time 0. For instance, r (1 , 2) is the interest rate of the second year, which is only know at time 1 (the beginning of the second year). ABC is facing interest rate risk , the risk that these future interest rates go up and thus ABS needs to pay more interest on the debt. 8.1.2 To reduce the risk, ABC can enter into a swap in which they receive a floating rate and pay some fixed rate R , so that the swap payoff at the end of the i-th year is Swap payoff at the end of the i-th year = A · ( r ( i- 1 ,i )- R ) , i = 1 , 2 ,...,n. With this swap, the net cashflow of ABC at the end of each year is now fixed: Net cashflow at the end of the i-th year =- A · r ( i- 1 ,i ) | {z } Original cashflow + A · ( r ( i- 1 ,i )- R ) | {z } Swap payoff =- A · R. Now ABC is like paying a fixed rate R instead of a floating rate, so the interest rate risk is eliminated. The fixed rate R is called the swap rate . Original CF =- floating New CF =- floating + ( floating- fixed) | {z } CF from swap =- fixed STAT 2820 Chapter 8 2 8.1.3 The table in 8.1.1 now becomes: Time Interest payment after using swap Principal paid 1 AR , as the interest for the first year 2 AR , as the interest for the second year . . . . . . n- 1 AR , as the interest for the ( n- 1)-th year n AR , as the interest for the n-th year A Notice two features from this table: • All interest payments do not depend on future interest rates r (1 , 2) ,r (2 , 3) etc. Hence there is no uncertainty. • As the annual interest payments are always AR , ABC is effectively paying an interest rate of R per year. This rate R does not change during the life of the loan (swap)....
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Lecture08[1] - STAT 2820 Chapter 8 Interest Rate Swaps by...

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