# Swaps in Finance | Definition | Examples |Valuation

The very Basic English meaning of Swap is exchange or exchange a thing in return of another. In finance, Swaps definition is nothing but the exchange of cash flows. Or in other words, we can define it as an OTC derivative contract between two parties exchanging a sequence of cash flows with another at a predetermined rate in the future period mutually agreed between them.

## What are Swaps?

Let us understand swaps with an help of an example.

EDU Inc. enters into a financial contract with CBA Inc. in which they have agreed to exchange a cash flows making LIBOR as its benchmark wherein EDU Inc. will pay a fixed rate of 5% and receive a floating rate of LIBOR+2% from CBA Inc.

Now if we see, in this financial contract there are two legs of transaction for both the parties.

• EDU Inc. is paying fixed rate of 5% and receiving floating rate (Annual LIBOR+2%) whereas CBA Inc. is paying floating rate (Annual LIBOR+2%) and receiving fixed rate (5%).

In order to understand this, let’s look into the numerical now.

In the above example, let’s assume that both the parties have entered into swaps contract for one year with a notional principal of Rs.1,00,000/-(since this is an Interest rate swap, hence the principal will not be exchanged). And after one year, the one year LIBOR in the prevailing market is 2.75%.

We will analyze the cash flows for two scenarios:

1. When the one year LIBOR is 2.75%,
2. When the one year LIBOR increased by 50 bps to 3.25%

#### Scenario 2 (When one year LIBOR is 3.25%)

Looking at the above exchange of cash flows, an obvious question comes to our mind that why financial institutions enters into swaps agreement.It is clearly seen in the scenario 1 that fixed paying party is benefitted from the swaps. However, when the one year LIBOR increased by 50 bps to 5.25%, it was in loss from the same swap agreement.

The answer to this is comparative rate advantage to both the parties.

## Swaps – Comparative Rate Advantage

The comparative rate advantage suggests that when one of the two borrowers has a comparative advantage in either the fixed or floating rate market they better off their liability by entering into swaps. It basically reduces the cost of both parties. However, comparative advantage argument assumes that there is no credit risk involved and funds can be borrowed during the life of the swap.

To understand the comparative rate advantage, let’s assume that the EDU Inc. and CBA Inc. have their own borrowing capacities in both fixed as well as floating market (as mentioned in table below).

 Company Fixed Market Borrowing Floating Market Borrowing EDU Inc. 4.00% One year LIBOR-0.1% CBA Inc. 5.20% One year LIBOR+0.6%

In the above table, we can see that EDU Inc. has an absolute advantage in both the market, whereas CBA Inc. has a comparative advantage in floating rate market (as CBA Inc. is paying 0.5% more than EDU Inc.). Assuming both the parties have entered into a Swap agreement with the condition that EDU Inc. will pay one year LIBOR and receive 4.35% p.a.

The cash flows for this agreement are described in the table below for both the parties.

 Cash Flows for EDU Inc. Receivable in Swap agreement 4.35% Payable in Swap agreement LIBOR Payable in fixed market borrowing 4.00% Net Effect LIBOR-0.35% Cash Flows for EDU Inc. Receivable in Swap agreement LIBOR Payable in Swap agreement 4.35% Payable in floating market borrowing LIBOR+0.6% Net Effect 4.95%

Looking at the above cash flows, we can say that EDU Inc. has a net cash flow of LIBOR – 0.35% per annum giving it an advantage of 0.25%, which EDU Inc. had to pay if it went directly in the floating market i.e. LIBOR – 0.1%.

In the second scenario for CBA Inc., the net cash flow is 4.95% per annum giving it an advantage of 0.25% in fixed borrowing market, if it had gone directly i.e. 5.20%.

## Types of Swaps

There are several types of Swaps transacted in the financial world. They are commodity swaps, equity swaps, volatility swaps, debt swaps, credit default swaps, puttable swaps, swaptions Interest rate swap, currency swap etc.

## Valuation of Swaps

As we know that Swap is nothing but the series or a combination of bonds for both counter parties and hence its valuation is also easy.

For example suppose that two counter parties A and B enter into Swaps agreement wherein A pays fixed and receive float (refer image: 2 below). In this arrangement, if we see there is a package of two bonds for A.

1. A is short on fixed coupon paying bond and
2. Long on floating coupon paying bond.

At any given point of time, value of the swap for a fixed rate payer is the difference between the present value of the remaining floating rate payment and present value of the remaining fixed rate payment (Bfloat – Bfixed). Whereas for a fixed rate receiver, value of the swap is the difference between the present value of the remaining fixed rate payment and present value of the remaining floating rate payment (Bfixed – Bfloat). We can calculate value of swap for either of the party and then find out for another easily as swap is a derivative contract and we are aware that derivative is a zero sum game wherein profit for one party is equal and opposite to the loss of another. Hence, formula for value of swap agreement can be summarized as below:

• Value of a Swap agreement (for a Floating rate payer) = PV of remaining fixed rate payment (Bfixed) – Value of remaining floating rate payment (Bfloat) or Bfixed – B
• Value of a Swap agreement (for a Fixed rate payer) = PV of remaining float rate payment (Bfloat) – Value of remaining fixed rate payment (Bfixed) or Bfloat – B

Here, one point is to be noted that at the date of settlement, value of floating coupon bond is always equal to the notional principal as at the date of settlement coupon rate is equal to YTM or the bond is par bond.

## Swaps Valuation – Example

Suppose A & B enters into a Swap Agreement for two years wherein A pays fixed (here A is short on fixed coupon paying bond) at the rate of 4% and receives LIBOR from B. One year has already crossed and both the party wants to terminate the agreement immediately.

Notional principal is Rs.1,00,000/- and two year LIBOR is 4.5%.

#### Scenario -1 (if party A pays fixed)

Here, since the swap agreement was supposed to end after two years but it is being terminated by the counterparties only after one year. Hence, we have to value the swap at the end of one year.

As per the above formula, value of swap = Bfloat – Bfixed, Where,

Bfloat = PV of all remaining float rate payment and,
Bfixed = PV of remaining fixed rate payment.

Calculations:

Bfloat= since we are valuing the Swap at the date of settlement, the PV of floating rate payment would be the notional principal i.e. Rs.100000/-. Also, it is assumed that on the date of settlement, coupon payment has been made to long party.

Hence, Bfloat = Rs.100000/-

Bfixed = The total fixed payment to be made by A for second year is principal of Rs.100000/- and interest of Rs.4000/- (100000*0.04). This amount needs to be discounted with two year LIBOR i.e. 4.5%.

(P+C)*e-r*t = (100000+4000)*e-0.045*1

= 99423.74

Hence, Bfixed = 99423.74

Value of Swaps = Rs.100000 – Rs.99423.74

= Rs.576.26

#### Scenario -2 (if party A pays float)

As per the above formula, value of swap = Bfixed – Bfloat,

Calculations:

Bfloat= Here also the PV of floating rate payment would be the notional principal i.e. Rs.100000/- as we are valuing the swap at the date of settlement.

Hence, Bfloat = Rs.100000/-.

Bfixed = The total fixed payment to be made by B for second year is principal of Rs.100000/- and interest of Rs.4000/- (100000*0.04). We will discount this amount with two year LIBOR i.e. 4.5%.

(P+C)*e-r*t = (100000+4000)*e-0.045*1

= 99423.74

Hence, Bfixed = 99423.74

Value of Swaps = Rs.99423.74 – Rs.100000

= – Rs.576.26

In the above-explained scenarios, we have seen the valuation of Swaps on the date of settlement. But what if, the contract is not terminated on the date of settlement?

## Valuation of Swaps – Before the date of settlement

Let’s see how valuation is done in case the contract is not terminated on the date of settlement.

The valuation for fixed leg payment shall remain same as explained above. But valuation for floating leg is slightly changed. Here, since we are not standing on the date of settlement, the discounting for floating rate payment shall be Notional Principal + Floating rate payment for the remaining period.

Let’s look at the example.

Suppose A & B enters into a Swap Agreement for two years wherein A pays fixed (here A is short on fixed coupon paying bond) at the rate of 4% and receives LIBOR from B. After one and half years both the party wants to terminate the agreement immediately.

Notional principal is Rs.1,00,000/- and two year LIBOR is 4.5%.

Value of Swaps = Bfloat – Bfixed, Where,

Bfloat = PV of all remaining float rate payment and,
Bfixed = PV of remaining fixed rate payment.

Bfloat= since valuation is happening six months prior to the settlement, the PV of floating rate payment would be the notional principal i.e. Rs.100000/- plus the floating rate coupon payment which is due in next six months. The same can be found out using two years LIBOR curve.

(P+C)*e-r*t = (100000 + 4500)* e-0.045*0.5

= 102175.00

Hence, Bfloat = Rs.102175.00

Bfixed = Total fixed payment to be made by A for second year is principal of Rs.100000/- and interest of Rs.4000/- (100000*0.04). This amount needs to be discounted with two year LIBOR i.e. 4.5% for six months as six months are left to expire the contract.

(P+C)*e-r*t = (100000+4000)*e-0.045*0.5

= 101686.12

Hence, Bfixed = 101686.12

Value of Swaps = Rs.102175 – Rs.101686.12

= Rs.488.88

## What are Currency Swaps?

Like an Interest rate swap (as explained above), Currency Swaps (also known as Cross Currency Swaps) is a derivative contract to exchange certain cash flows at a predetermined time. The basic difference here is, under currency swaps, the principal is exchanged (not obligatory) at inception as well as at maturity of the contract and cash flows are in the different currencies, therefore, generate a larger credit exposure.

Another difference between these types of swaps are, in Interest Rate swap, cash flows are netted at the time of settlement whereas, in the currency swap, the same is not netted but exchanged in actual between parties.

## Mechanics of currency swaps

Suppose two companies EDU Inc. (based in US) and CBA Inc. (based in India) entered into a currency swaps, wherein EDU Inc. pays 5% in INR and receives 4% in USD (and CBA Inc. pays 4% in USD and receives 5% in INR) every year for the next two years (refer Image: 3). In the beginning of the contract both the parties exchanged certain amount of principals (EDU Inc. exchanged USD 80000 and CBA Inc. exchanged INR 100000). The current spot rate is INR 65/USD.

Here, at each settlement date EDU Inc. shall pay INR 5000 (100000*0.05) to CBA Inc. and receives USD 3200 (80000*0.04) from CBA Inc. respectively. Further, at the end of the contract both the parties shall exchange the principal amount i.e. EDU Inc. shall pay INR 100000 and CBA Inc. shall pay USD 80000.

## Valuation of Currency Swaps

Currency swaps are valued in the same way as interest rate swaps, using discounted cash flows (bond method). Hence,

Value of Currency Swaps (long on one bond) = Blong on currency – So*Bshort on currency,

Value of Currency Swaps (short on one bond) = Bshort on currency – So*Blong on currency, where

S0 = Spot rate of the currency

Let’s understand this through a numerical.

Taking the above example into consideration, assume that the interest rate in the India is 6% and in USA is 4%. Assume that the interest rate remains constant throughout the life of Swaps agreement in both the economy. Exchange rates for the currencies are INR 65/USD.

Before proceeding to value the swap contract, first look at the cash flows in below table:

* Discounting factor is arrived through formula e-r*t

# PV of Cash flows are arrived through formula Cash Flows*Discounting Factor

As mentioned above the valuation of currency swaps is also done through discounted cash flow. Therefore, here we will calculate the total PV of Cash flows in both the currencies.

PV of INR Cash Flows = INR 53820.36

PV of USD Cash Flows = USD 28182.30

Since, EDU Inc. is long on USD and short on INR, therefore,

Value of Swaps = BUSD – S0*BINR

= 28182.30 – (1/65)*53820.36

= 28182.30 – 828.01 = 27354.49

## In a Nutshell

• Swaps is an OTC derivative contract between two parties exchanging a sequence of cash flows with another at a predetermined rate for a set period of time.
• Under Swaps agreement, one party exchange fixed cash flows in return of floating cash flows exchanged by the other counter party.
• The most common kind of swaps is the Interest rate swaps and Currency swaps
• A plain vanilla interest rate swap exchanges fixed rate payment for floating rate payment over a period of swaps.
• A swap contract is equivalent to a simultaneous position in two bonds.
• The comparative rate advantage suggests that when one of the two borrowers has a comparative advantage in either the fixed or floating rate market they better off their liability by entering into the swap.
• The value of the swap for a fixed rate receiver is the difference between the present value of the remaining fixed rate payment and present value of the remaining floating rate payment and for a floating rate receiver is the difference between the present value of the remaining floating rate payment and present value of the remaining fixed rate payment.
• Currency swaps exchanges cash flows in different currencies along with the principal amount at inception and at maturity, though not obligatory.
• Types of Swaps are commodity swaps, equity swaps, volatility swaps, debt swaps, credit default swaps, puttable swaps, swaptions etc.

1. By Austin LYNCH on

I was trying to understand the whole concept of Swap Rate and couldn’t find a good explanation on swap rate. If you could tell me what actually Swap Rate Is? It will be very helpful.

• Swaps are those derivatives where counterparts exchange fixed payment against floating rate payments. A Swap is an agreement between two parties where future interest payments are exchanged for another based on a specified principal amount. Final answer to your question is that the fixed rate which you agree to pay is called the Swap Rate.

2. By Noah HENRY on

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• Thanks Noah! I am glad that you found my blog useful, well if you are about to start a Finance business. I must tell you Making money through financing takes time, but you can start many types of financing business, if you are thinking to start any kind of finance firm license is an essential requirement to start any finance firm.
If you want to know anything more I’ll be glad to comment further.