Explain why margin accounts are only required when clients write options but not when they buy options?

Chapter8-Swaps-Students.pptx

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Chapter 8 Swaps

Nature of Swaps

A swap is an agreement to exchange cash flows at specified future times according to certain specified rules

A swap is just a series of forward contracts

Typically one party pays a fixed rate/payment and the other party pays a variable rate/payment depending on an unknown component (i.e. interest rate, exchange rate or price), but can be for a commodity

Characteristics of a Swap

Like a forward, a swap typically has a value of zero at the start of the contract

No party pays any amount to the other party (exception is currency swaps where each party pays the notional principal to the other party, while the payments are equivalent they are in difference currencies)

Settlement date occurs each time (date) both parties make payments

The last payment date is called the termination date

Typically both parties agree to exchange only the net amount owed, i.e. only one cash flow occurs

This practice is called netting

Almost all swaps are cash settlement

Swaps tend to be traded over-the counter (OTC)

An Example of a “Plain Vanilla” Interest Rate Swap

Plain Vanilla Swap – An interest rate swap which one party pays a fixed rate and the other party pays a floating rate with both payments made in the same currency

The most common derivative transaction worldwide

On March 5, 2012 – An agreement by Microsoft to receive 6-month LIBOR & pay a fixed rate of 5% per annum every 6 months for 3 years on a notional principal of $100 million

Next slide illustrates cash flows that could occur (Day count conventions are not considered)

One Possible Outcome for Cash Flows to Microsoft

Date	LIBOR	Floating Cash Flow	Fixed Cash Flow	Net Cash Flow
Mar 5, 2012	4.20%
Sep 5, 2012	4.80%	+2.10	−2.50	−0.40
Mar 5, 2013	5.30%	+2.40	−2.50	−0.10
Sep 5, 2013	5.50%	+2.65	−2.50	+ 0.15
Mar 5, 2014	5.60%	+2.75	−2.50	+0.25
Sep 5, 2014	5.90%	+2.80	−2.50	+0.30
Mar 5, 2015		+2.95	−2.50	+0.45

Typical Uses of an Interest Rate Swap

Converting an investment or a liability from

fixed rate to floating rate

floating rate to fixed rate

Using a Swap to Transform a Liability

Intel pays interest of 5.2%

Wants to pay floating

Microsoft pays interest of LIBOR + 10 basis points(0.01%)

Wants to pay fixed

Intel and Microsoft (MS) Transform a Liability

Intel

LIBOR

LIBOR+0.1%

5.2%

Using a Swap to Transform a Liability

Intel receives interest of 4.7%

Wants to receive floating

Microsoft receives interest of LIBOR – 20 basis points

Wants to receive fixed

Intel and Microsoft (MS) Transform an Asset

Intel

LIBOR

LIBOR-0.2%

4.7%

Financial Intermediary

Typically firms do not find each other but instead go to a financial intermediary to take the other position

A financial intermediary typically looks to enter into two offsetting swaps

Financial intermediary typically makes 3 or 4 basis points on the two swaps combined

The financial intermediary is still exposed to the possibility that one party may default

Has no impact on the other swap

Financial Institution is Involved

F.I.

LIBOR

LIBOR+0.1%

4.985%

5.015%

5.2%

Intel

Financial Institution has two offsetting swaps

Financial Institution is Involved

F.I.

Intel

LIBOR

4.7%

5.015%

4.985%

LIBOR-0.2%

Quotes By a Swap Market Maker

Maturity	Bid (%)	Offer (%)	Swap Rate (%)
2 years	6.03	6.06	6.045
3 years	6.21	6.24	6.225
4 years	6.35	6.39	6.370
5 years	6.47	6.51	6.490
7 years	6.65	6.68	6.665
10 years	6.83	6.87	6.850

Day Count

A day count convention is specified for fixed and floating payment

For example, LIBOR is likely to be actual/360 in the US because LIBOR is a money market rate

In many cases the fixed rate is quoted as actual/365 or 30/360

Fixed payment each time could change slightly depending on the actual day count

Results in the rates not always directly comparable to LIBOR

Confirmations

Confirmations specify the terms of a transaction (i.e. legal agreement)

The International Swaps and Derivatives Association has developed Master Agreements that can be used to cover all agreements between two counterparties

The Comparative Advantage Argument

AAACorp wants to borrow floating

BBBCorp wants to borrow fixed

	Fixed	Floating
AAACorp	4.0%	6 month LIBOR − 0.1%
BBBCorp	5.2%	6 month LIBOR + 0.6%

The Swap

AAACorp

BBBCorp

LIBOR

LIBOR+0.6%

4.35%

The Swap with a Financial Institution is Involved

AAACorp

F.I.

BBBCorp

LIBOR

LIBOR+0.6%

4.33%

4.37%

Criticism of the Comparative Advantage Argument

The 4.0% and 5.2% rates available to AAACorp and BBBCorp in fixed rate markets are 5-year rates

The LIBOR−0.1% and LIBOR+0.6% rates available in the floating rate market are six-month rates and are typically able to be adjusted every 6-months

Swap Benefits

BBBCorp if it continues to borrow at LIBOR+0.6%

AAACorp only pays LIBOR – 0.33% but now exposed to risk of default

Interest Rate Swaps

Typically the notional principle is not exchanged

Notional principles are the same so if they did swap it, it has zero impact on the swap but it makes the valuation of the swap easier

Fixed rate is now like a coupon bond

At any point we only know the next floating payment that will be made

At start and at every payment the coupon rate for the next floating rate resets and the floating rate equals the fixed

Interest Rate Swaps

At the start:

n is the expiration of the swap

m is time interval between payments

Interest Rate Swap – Example

What should the fixed payment be for a one-year swap with quarterly payments on days 90, 180, 270, & 360, with the underlying being the 90-day LIBOR. The swap is for $30,000,000 in notional principal. The annualized current LIBOR spot rates today quoted per annum with continuous compounding are:

L0(90) = 0.0345

L0(180) = 0.0358

L0(270) = 0.0370

L0(360) = 0.0375

Interest Rate Swap – Example

Use Continuous compounding

B0(90) = 0.9914

B0(180) = 0.9823

B0(270) = 0.9726

B0(360) = 0.9632

Annualized the rate is 3.77%

It is worth taking a second for you to verify that the value of the swap is zero when it is entered into

Valuation of an Interest Rate Swap

Initially interest rate swaps are typically worth zero

As time goes on they can be valued as:

The difference between the value of a fixed-rate bond and the value of a floating-rate bond

They can be valued as a portfolio of forward rate agreements (FRAs)

Valuation in Terms of Bonds

The fixed rate bond is valued in the usual way

The floating rate bond is valued by noting that it is worth par immediately after the next payment date

Similar to a bond with only its last payment left (interest (k*) and principle (L))

Valution of Floating-Rate Bond

Valuation Date

First Pmt

Date

Floating Pmt =k*

Second

Pmt Date

Maturity Date

Value = L

Value = L+k*

Value = PV of L+k* at t*

Example

You pay six-month LIBOR, receive 8% (s.a. compounding) and on a principal of $100 million

Remaining life 1.25 years

LIBOR rates for 3-months, 9-months and 15-months are 10%, 10.5%, and 11% (cont comp)

6-month LIBOR on last payment date was 10.2% (s.a. compounding)

Valuation Using Bonds

Time	Bfix Cash Flow	Bfl Cash Flow	Disc Factor	PV Bfix	PV Bfl
0.25	4.0	105.100	0.9753	3.901	102.505
0.75	4.0		0.9243	3.697
1.25	104.0		0.8715	90.640
Total				98.238	102.505

Swap value = 98.238 − 102.505 = −4.267

Valuation in Terms of FRAs

Each exchange of payments in an interest rate swap is an FRA

A swap is just a portfolio of FRAs

But the predetermined fixed rate is the same for all payments

The FRAs can be valued on the assumption that today’s forward rates are realized

Valuation of Example Using FRAs

Time	Fixed Cash Flow	Floating Cash Flow	Net Cash Flow	Disc Factor	PV Bfl
0.25	4.0	-5.100	-1.100	0.9753	-1.073
0.75	4.0	-5.522	-1.522	0.9243	-1.407
1.25	4.0	-6.051	-2.051	0.8715	-1.787
Total					-4.267

Use the equation for RF to get the floating rate for 0.75 & 1.25 and convert from continuous compounding to semi annual compounding

Swap Value

Remember the value at t=0 is 0

This does not mean when looking at it as multiple FRAs that each FRA is worth 0, rather the sum of all FRAs is 0

Currency Swaps

It is common to pay the notional principal in a currency swaps as the payments are made in different currencies but are equal in value

Notional principle is 1 unit of domestic currency and 1/S0 unit of foreign currency

Notional principle can be S0 of domestic currency and 1 unit of foreign currency

In the cases where there is a fixed rate(s) the fixed rate(s) is the fixed rate(s) on the plain vanilla interest rate swaps in the respective country

Fixed Rate in a Currency Swaps

In the cases where there is a fixed rate(s) the fixed rate(s) are the fixed rate(s) on plain vanilla interest rate swaps in the respective country

Can also calculate as

Bi is the zero coupon bond for time i

FS* is the foreign rate

F0,i is the forward exchange rate at time i

S0 is spot exchange rate (domestic/foreign)

Currency Swaps

8 types of traditional currency swaps (Using $ & £)

Person A pays $ at a fixed rate and Person B pays £ at a fixed rate

Person A pays $ at a fixed rate and Person B pays £ at a floating rate

Person A pays $ at a floating rate and Person B pays £ at a floating rate

Person A pays $ at a floating rate and Person B pays £ at a fixed rate

Person B pays $ at a fixed rate and Person A pays £ at a fixed rate

Person B pays $ at a fixed rate and Person A pays £ at a floating rate

Person B pays $ at a floating rate and Person A pays £ at a floating rate

Person B pays $ at a floating rate and Person A pays £ at a fixed rate

Currency Swap

Fixed rate on plain vanilla swaps in domestic country makes the present value of the domestic interest and principle payments equals 1 unit of the domestic currency

A notional principle of 1/S0 unit of foreign currency makes the present value of the foreign interest and principle payments equals 1/S0 unit of the foreign currency

Conversion of the 1/S0 unit of foreign currency at the current exchange rate of S0 gives 1 unit of domestic currency

Therefore, the present value of the domestic payments equal the present value of the foreign payment

Typical Uses of a Currency Swap

Convert a liability in one currency to a liability in another currency

Convert an investment in one currency to an investment in another currency

An Example of a Currency Swap

An agreement to pay 5% on a sterling principal of £10,000,000 & receive 6% on a US$ principal of $18,000,000 every year for 5 years

The Cash Flows

Date	Dollar Cash Flows (millions)	Sterling Cash Flow (millions)
Feb 1, 2011	-18.0	+10.0
Feb 1, 2012	+1.08	−0.50
Feb 1, 2012	+1.08	−0.50
Feb 1, 2014	+1.08	−0.50
Feb 1, 2015	+1.08	−0.50
Feb 1, 2016	+19.08	−10.50

Valuation of Currency Swaps

Like interest rate swaps, currency swaps can be valued either as the difference between 2 bonds or as a portfolio of forward contracts

Example

All JPY LIBOR/swap rates are 4%

All USD LIBOR/swap rates are 9%

5% is received in yen; 8% is paid in dollars

Payments are made annually

Principals are $10 million and ¥1,200 million

Swap will last for 3 more years

Current exchange rate is ¥110/$1

Valuation in Terms of Bonds

Time	Cash Flows ($)	PV ($)	Cash Flows (¥)	PV (¥)
1	0.8	0.7311	60	57.65
2	0.8	0.6682	60	55.39
3	0.8	0.6107	60	53.22
3	10.0	7.6338	1,200	1,064.30
Total		9.6439		1,230.55

Value of Swap = 1230.55/110 − 9.6439 = $1.5430 million

Valuation in Terms of Forwards

Time	$ Cash Flow	¥ Cash Flow	Forward Exchange Rate	¥ Cash Flow in $	Net Cash Flow	Present Value (Mil $)
1	-0.8	60	0.009557	0.5734	-0.2266	-0.2071
2	-0.8	60	0.010047	0.6028	-0.1972	-0.1647
3	-0.8	60	0.010562	0.6337	-0.1663	-0.1269
3	-10.0	1200	0.010562	12.6746	2.6746	2.0417
Total						1.5430

Swaps & Forwards

A swap can be regarded as a convenient way of packaging forward contracts

Although the swap contract is usually worth nothing (i.e. zero) at the outset, each of the underlying forward contracts are not worth zero

Commodity Example

Let’s assume we are a small airline that expects to use 100,000 gallons of jet fuel each year

Rates are annual with continuous compounding

Credit Risk

A swap is worth zero to a company initially

At a future time its value is likely to be either positive or negative

The company has credit risk exposure only when its value is positive

Some swaps are more likely to lead to credit risk exposure than others

Currency swaps have greater credit risk than interest rate swaps

YearRateForward Price

15.0%1.576906645

25.50%1.674417106

36.50%1.822966480

Sheet1

Year	Rate	Forward Price
1	5.0%	1.576906645
2	5.50%	1.674417106
3	6.50%	1.822966480