Question

A 3-year interest rate swap has a level notional amount of $300,000. Each settlement period is one year and the variable rate is the one-year spot interest rate at the beginning of the settlement period. The current spot rate is determined by the following prices for zero-coupon bonds with $1 face amount:
Time of Maturity 1 Year 2 Year 3 Year 4 Year 5 Year
Price 0.97 0.93 0.88 0.82 0.75

Required:
a. Calculate the swap rate.
b. Caleulate the net swap payment at the end of the first year.
c. One year has elapsed and the one-year spot interest rate at the start of year 2 is 4.45%. Calculate the net swap payment at the end of the second year for the payer.
d. Two years have elapsed and the one-year spot interest rate at the start of year three is 5.25 Calculate the market value of the swap.

Answer 1

Answer:

(a)0.04317 (b) 3672 which will be paid by the payer to the receiver (c) -399. so, the 399 which will be paid by the receiver to the payer (d) 2659.38

Explanation:

Solution

(a) Swap Rate (R) = (1 - P₃)/(P₁+P₂+P₃)

= (1 – 0.88)/(0.97 + 0.93 + 0.88)

= 0.04317

(b) The payer pays the fixed interest rate and gets the variable interest rate.

Then, the fixed interest rate is known as the  swap rate which is 4.317%.

Now,

The variable rate is the one year spot rate for the first year of the loan. which is r₁ = 1/P₁ -1 = 1/0.97 - 1 = 0.03093

Thus,

The net swap payment becomes (300,000)(0.04317) - (300,000)(0.03093) = 3672 which will be paid by the payer to the receiver.

(c) The payer pays the fixed interest rate and receives the variable interest rate. The fixed interest rate is the swap rate which is 4.317%.

Thus,

The variable rate is the one year spot rate for the second year of the loan is 4.45%.

So,

The net swap payment becomes (300,000)(0.04317) - (300,000)(0.04450) = -399.

Therefore, the 399 which will be paid by the receiver to the payer.

(d) The market value is the present value of expected future cash flows. under this swap, the variable rate has been swapped for the constant swap rate. There is one year left under the swap.

Then,

The expectation is that the swap owner will pay (300,000)(0.04317) and receive (300,000)(0.0525). these payments would be made at the end of one year. Therefore, the market value will be:

{(300,000)(0.0525) - (300,000)(0.04317)}/1.0525 = 2799/1.0525 = 2659.38