A swap is simply an agreement between two companies to exchange cash flows in the future. The financial instrument is mostly cash flows based on notional principal amount that both parties agree to.

**Plain Vanilla Swaps**

In this type of swap, one party agrees to pay cash flows equal to the interest at a predetermined fixed rate of interest on a notional principal amount for a number of years and in return, the other party agrees to pay cash flows equal to the interest at a floating rate of interest on a notional principal amount for a number of years.

The floating rate in most interest rate swap agreements is LIBOR.

**Example:**

For example, consider company A has issued $500 million in 5-year bonds with a variable rate of interest as 6 month LIBOR+0.2% per annum. The bond will have 10 coupon payments and for each of the payments, the coupon is set 0.2% per annum above the 6-month LIBOR rate at the beginning of the period.

Consider that company B is willing to pay company A an annual rate of LIBOR+0.2% for 5 years on a notional principal of $500 million. In return, A pays B a fixed rate of 1.6% on the notional principal of $5 million for 5 years.

A is the *fixed rate payer* and B is the *floating rate payer*.

Consider that the above agreement took place on April 5, 2011. The first payment would be made on October 5, 2011. Consider that the LIBOR rate prevailing on April 5, 2017 to be 1.45%.

A pays B $4,000,000 (interest rate on $500 million at 1.6% for 6-month period) and B pays A $3,625,000 (interest rate on $500 million at LIBOR+0.2% for 6-month period). The next exchange of payments will be made in April, 2018. The net cash flow for A is $375,000. In all there will be 10 such cash flows.

This is how it would appear

It is equivalent to company A taking short position on fixed rate bond and taking a long position on a floating rate bond. Company B is taking a long position on fixed rate bond and taking a short position on a floating rate bond.

**Swap transforms liability**

A swap can be used to tranform a fixed rate of interest into a floating rate of interest and vice versa. In the above example, if we consider that company A borrowed $500 million at LIBOR+0.1%, then

Company A has the following cash flows:

- It pays LIBOR+0.1% to the outside lender
- It receives LIBOR+0.2% from B
- It pays 1.6% under the terms of the swap

The effective interest rate for company A is 1.5%.

Similarly, if we consider that company B borrowed $500 million at 1.8%, then

Company B has the following cash flows:

- It pays 1.8% to the outside lender
- It receives 1.6% from A
- It pays LIBOR+0.2% under the terms of the swap

The effective interest rate for company A is (LIBOR+0.4)%

**Basis Point**

It is a unit of measurement of the interest rate.

1 basis point = 0.01% (0.0001)

**Financial Intermediary**

When two non financial companies enter into a swap agreement, the deal is done through a financial intermediary like a bank or a financial institution. The financial institution in return for the services, earn anywhere between 3 or 4 basis points depending on the nature of the deal and the amount of money involved.

**Problem 7.1 from ‘Options, futures and other derivatives’ from John C. Hull**

Companies A and B have been offered the following rates p.a. for a $20 million five-year loan:

Fixed rate | Floating Rate | |

Company A | 5.0% | LIBOR + 0.1% |

Company B | 6.4% | LIBOR + 0.6% |

A requires floating rate loan and B required a fixed-rate loan. Intermediary bank will take 0.1% p.a.

Company A has comparative advantage in the fixed rate market and B has a comparative advantage in the floating rate market.

Fixed rate differential = 1.4%

Floating rate differential = 0.5%

Total gain to all parties = 0.9%

Bank will get 0.1% and each of company A and company B will get 0.4%.

Hence, company A can borrow at LIBOR – 0.3%

Company B can borrow at 6%.

**Market Makers**

In practice it is not possible for 2 companies to contact the same financial institution at the same time to facilitate a swap. So, most of the times, a large financial institution works as market makers for swaps. So, they enter into a swap without having an offsetting swap at the same time. So,a financial institution can **bid and offer fixed rates for a swap and a swap rate is the average of the bid and offer rates**.

As mentioned earlier, a swap can be considered as the difference of a floating rate bond and a fixed rate bond.

Let,

B_{fix} = value of the fixed-rate bond

B_{fl} = value of the floating rate bond

The swap is worth zero when,

B_{fix} = B_{fl}

**Comparative Advantage**

Some companies have an advantage when it comes to borrowing in fixed-rate markets, while some other companies have an advantage whil borrowing in floating rate market. Some companies might have a comparative advantage in some currency as compared to a different currency. For loans, it is advisable for companies to go to markets where they have comparative advantage.

Consider the following rates

Fixed | Floating | |

Company A | 4.5% | LIBOR – 0.2% |

Company B | 5.7% | LIBOR+0.5% |

Company A clearly has a comparative advantage in fixed rate market while company B has a comparative advantage in floating rate market. Now if company B wants a fixed rate and company A wants a floating rate, there is the possibility of a swap occurring.

**LIBOR/Swap zero rates**

As mentioned earlier, a swap can be viewed as an exchange of a fixed rate bond with a floating rate bond. This means that the swap rate defines par yield bonds and hence can be used to bootstrap the LIBOR/Swap zero curve

Example 7.1 from ‘Options, Futures and other derivatives’ by John C. Hull

Suppose that the 6-month, 12-month and 18-month LIBOR/Swap zero rates are 4%, 4.5% and 4.8% with continuous compounding and that the 2-year swap rate (where payments are made semiannually) is 5%. Find the 2-year zero rate?

The bond pays 2.5 every 6 months.

Hence,

2.5e^{(─0.04×0.5)} + 2.5e^{(─0.045×1.0)} + 2.5e^{(─0.048×1.5)} +102.5e^{(─R×2)} = 100

Solving for R we get, R = 4.953% (2 year zero rate)