Deck 5: Interest Rate Derivatives: Forwards and Swaps

Question 1

Determine the swap rate for the following maturities: 0.25, 0.50, 0.75, 1.00, 1.50, 2.00. Use the following discount factors:

Answer 1

The values are c(0.25) = 6.50%, c(0.50) = 6.56%, c(0.75) = 6.61%, c(1.00) = 6.67%, c(1.50) = 6.78%, c(2.00) = 6.84%.

Question 2

Use the following table when needed:
What is a forward discount factor?

Answer 2

Question 3

Consider the same swap as in the previous question. What is the value of the swap three months after initiation, where the discount factors are now:

Answer 3

The value of the swap is now: 222,408.

Question 4

What is the Forward Price to purchase a 1.5-year ?xed rate Treasury paying 5% semiannually, a year from now? At t = 0 we have the following discounts:

Question 5

Suppose you have entered into the Forward Contract from the previous ex- ercise, what is the value of the contract 6-months after initiation? Assume that the discount factors are now the ones presented at the beginning of this section.

Question 6

Use a swap to hedge the following Balance Sheet, so that parallel shifts in the term structure don't have an impact on the equity value: The swap used to hedge is 1.5 year swap, you know the following discount factors: In order to get the answer, compute the following:
i. What is the adequate swap rate?
ii. What is the dollar duration of the swap?
iii. What is the value of equity and its dollar duration, prior to any hedging?
iv. What is the value of notional needed so that the swap position hedges any impact that parallel shifts in the yield curve may have on the value of equity?

Question 7

You notice that forward rates are below the spot rate. What can you say about the yield curve?

Question 8

Assume that the swap spread at the moment is large, compared to histor- ical data. What would your expectations be? Will it increase, decrease or stay the same? To what extent?

Question 9

If short term rates go up, what would happen to the swap rate?

Question 10

What is the value of a swap at initiation?

Question 11

Value a 1.5 year swap, with swap rate 5.52%. Notional is 100 million. Use the following discount factors. You are told that this is a swap at initiation. Is the value accurate? Be sure to take into account any payment frequency conventions on the swap.

Question 12

The term structure of interest rates can be upward sloping or downward sloping. If this is so, can discount factors also be upward sloping or down- ward sloping?

Question 13

Determine the swap rate for the following maturities: 0.50, 1.00, 1.50, 2.00. Use the discount factors provided at the beginning of this section.

Question 14

Today you notice that forward rates are well above the spot rate. What shape must the yield curve have?

Question 15

Compute F (0, 3, 5), f2(0, 3, 5) and f(0, 3, 5).