Pricing and Valuation of Interest Rate and Other Swaps

50 questions available

Swaps versus Forward Rate Agreements5 min
An interest rate swap is conceptually a portfolio of forward contracts. While a standard strip of forwards would have different rates for each maturity to ensure each contract has zero value, a swap enforces a single fixed rate across all periods. Consequently, the individual forward components (FRAs) embedded in the swap are 'off-market'—some have positive value and some negative, summing to zero at initiation. A payer swap corresponds to a series of long off-market FRAs, engaging in a commitment to pay a fixed price for the underlying reference rate.

Key Points

  • Interest rate swaps are equivalent to a series of off-market FRAs.
  • Payer swap = Series of Long FRAs.
  • Receiver swap = Series of Short FRAs.
  • Off-market FRAs do not necessarily have a value of zero at initiation individually.
Pricing and Valuation Concepts6 min
The 'Swap Price' refers to the fixed rate ($sN$) set at the start of the contract. This rate is derived using the term structure of interest rates (spot rates $z_1, z_2...$) to equate the fixed leg's value to par. The 'Swap Value' represents the contract's worth to a party at any given time, calculated as the sum of the current settlement value and the present value of all future settlements. At the very beginning, the swap price is set such that the swap value is zero.

Key Points

  • Swap Price (Par Swap Rate) is the fixed rate equating fixed and floating legs.
  • Swap Value is the MTM value, which is zero at initiation.
  • Periodic Settlement = (MRR - Fixed Rate) * Notional * Period.
  • Valuation involves discounting future net settlements.

Questions

Question 1

To which of the following is an interest rate swap considered equivalent?

View answer and explanation
Question 2

What type of FRAs are used to replicate an interest rate swap?

View answer and explanation
Question 3

A payer swap can be replicated by using a series of:

View answer and explanation
Question 4

A receiver swap can be replicated by using a series of:

View answer and explanation
Question 5

What characterizes an 'off-market' FRA?

View answer and explanation
Question 6

The swap price is also known as the:

View answer and explanation
Question 7

Which formula best represents the calculation of the Swap Price ($s_N$)?

View answer and explanation
Question 8

What is the value of a plain vanilla interest rate swap at initiation?

View answer and explanation
Question 9

The Swap Value at any given time after initiation is composed of:

View answer and explanation
Question 10

Which component determines the 'Periodic Settlement Value' for the payer of the fixed rate?

View answer and explanation
Question 11

If the Market Reference Rate (MRR) is 5 percent and the Swap Fixed Rate is 4 percent, what is the nature of the periodic settlement for the fixed-rate payer?

View answer and explanation
Question 12

What does 'MRR' stand for in the context of swap settlement?

View answer and explanation
Question 13

Given a notional of 1,000,000 EUR, a fixed swap rate of 3 percent, an MRR of 4 percent, and a period of 1 year, what is the settlement value for the fixed-rate payer?

View answer and explanation
Question 14

Implied Forward Rates (IFRs) are derived from:

View answer and explanation
Question 15

Mark-to-Market (MTM) Value of a swap reflects:

View answer and explanation
Question 16

When calculating the par swap rate, the fixed leg is effectively treated as:

View answer and explanation
Question 17

If interest rates rise after the initiation of a receiver swap (receiving fixed), what happens to the value of the swap for the receiver?

View answer and explanation
Question 18

If a swap has a fixed rate of 4 percent and the MRR is 3 percent for a given period, which party makes the net payment?

View answer and explanation
Question 19

The 'tenor' of a swap refers to:

View answer and explanation
Question 20

In the swap price formula, what does 'PMT' represent?

View answer and explanation
Question 21

What is the primary role of spot rates ($z_1, z_2...$) in swap pricing?

View answer and explanation
Question 22

A swap with a fixed rate of 5 percent has a periodic settlement value of zero when:

View answer and explanation
Question 23

In the replication of a swap using FRAs, why are the FRAs considered 'off-market'?

View answer and explanation
Question 24

If the present value of the fixed leg exceeds the present value of the floating leg, the value of the swap to the fixed-rate payer is:

View answer and explanation
Question 25

For a receiver swap (receives fixed, pays floating), the value is positive if:

View answer and explanation
Question 26

Which factor is NOT explicitly required in the 'Swap Price' formula presented?

View answer and explanation
Question 27

Calculate the net payment for a fixed-rate payer on a 10 million USD swap with semi-annual payments (0.5 year period), where MRR is 4 percent and Fixed Rate is 4.5 percent.

View answer and explanation
Question 28

How is the 'Current Settlement Value' treated in the calculation of total Swap Value?

View answer and explanation
Question 29

What implies that the fixed rate of a swap ($s_N$) is the 'Par Swap Rate'?

View answer and explanation
Question 30

Which of the following describes the replication of a swap using FRAs?

View answer and explanation
Question 31

If the term structure is flat at 5 percent (all spot rates are 5 percent), what is the swap fixed rate?

View answer and explanation
Question 32

When calculating swap value, future floating cash flows are usually estimated using:

View answer and explanation
Question 33

What happens to the value of a payer swap if the yield curve shifts downward?

View answer and explanation
Question 34

The periodic settlement formula for a receiver of the fixed rate is:

View answer and explanation
Question 35

Which of the following is true regarding the notional amount in an interest rate swap?

View answer and explanation
Question 36

A 'Long' off-market FRA position effectively means:

View answer and explanation
Question 37

How does the 'Period' factor affect the settlement payment?

View answer and explanation
Question 38

If $z_1 = 5$ percent and $z_2 = 6$ percent, and the swap pays annual coupons for 2 years, the discount factor for the second cash flow is calculated as:

View answer and explanation
Question 39

Which valuation approach is consistent with the 'Law of One Price'?

View answer and explanation
Question 40

In the formula for Swap Price, the term 'PMT' is constant for:

View answer and explanation
Question 41

If a swap is valued at zero at initiation, what must be true about the fixed and floating legs?

View answer and explanation
Question 42

For a 1-year annual swap where the 1-year spot rate is 10 percent, what is the swap fixed rate?

View answer and explanation
Question 43

The value of a swap changes over time due to:

View answer and explanation
Question 44

Which term describes the net payment made on a settlement date?

View answer and explanation
Question 45

If implied forward rates (IFRs) increase, the calculated par swap rate for a new swap would likely:

View answer and explanation
Question 46

In a swap, the 'floating rate' is typically based on:

View answer and explanation
Question 47

What is the key difference between a standard FRA and a swap settlement period?

View answer and explanation
Question 48

If a 2-year swap has a fixed rate of 4 percent, and the 1-year spot rate is 4 percent, what does this imply about the 2-year spot rate?

View answer and explanation
Question 49

Why is the fixed rate in a swap sometimes called a 'par' rate?

View answer and explanation
Question 50

When calculating the payment on a swap, if the Period is 90 days and the convention is 360 days, the factor is:

View answer and explanation