Currency Futures, Options & Swaps

Reading: Chapters 7 & 14 (474-485)

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Lecture Outline

Introduction to Derivatives Currency Forwards and Futures Currency Options Interest Rate Swaps Currency Swaps Unwinding Swaps

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Introduction

A derivative (or derivative security) is a financial instrument whose value depends on the value of other, more basic underlying variables/assets: Share options (based on share prices) Foreign currency futures (based on exchange rates)

These instruments can be used for two very distinct management objectives: Speculation – use of derivative instruments to take a

position in the expectation of a profit. Hedging – use of derivative instruments to reduce the risks

associated with the everyday management of corporate cash flow.

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Definition of Futures and Forwards

Currency futures and forward contracts both represent an obligation to buy or sell a certain amount of a specified currency some time in the future at an exchange rate determined now.

But, futures and forward contracts have different characteristics.

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Futures versus Forwards

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Futures Contract - Example

Specification of the Australian Dollar futures contract (International Money Market at CME)

Size AUD 100,000Quotation USD / AUDDelivery Month March, June, September,

December Min. Price Move $0.0001 ($10.00)Settlement Date Third Wednesday of delivery

monthStop of Trading Two business days prior to

settlement date

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Futures - The Clearing House

When A “sells” a futures contract to B, the Clearing House takes over and the result is: A sells to the Clearing House

Clearing House sells to B

The Clearing House keeps track of all transactions that take place and calculates the “net position” of all members.

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Futures - Marking to Market

Futures contracts are “marked to market” daily. Generates cash flows to (or from) holders of foreign

currency futures from (or to) the clearing house. Mechanics:

Buy a futures contract this morning at the price of f0,T

At the end of the day, the new price is f1,T

The change in your futures account will be:

[f1,T - f0,T] x Contract Face Value = Cash Flow

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Purpose of Marking to Market

Daily marking to market means that profits and losses are realized as they occur. Therefore, it minimizes the risk of default.

By defaulting, the investor merely avoids the latest marking to market outflow. All previous losses have already been settled in cash.

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Marking to Market – Example

Trader buys 1 AUD contract on 1 Feb for USD0.5000/AUD

USD value = 100,000 x 0.5000 = USD 50,000.

Date Settlement Value of Contract Margin A/c________________________________________________________________________________

1 Feb 0.4980 49,800 - 200

2 Feb 0.4990 49,900 + 100

3 Feb 0.5020 50,200 + 300

4 Feb 0.5010 50,100 - 100

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Trouble with Forwards/Futures?

$ Spot

1.80

A$ 1.90/US$

Forward/FuturesRate

Seller (short)US$

Buyer (long)US$

0

+

-

2.00

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Basics of Options

Options give the option holder the right, but not the obligation to buy or sell the specified amount of the underlying asset (currency) at a pre-determined price (exercise or strike price).

The buyer of an option is termed the holder, while the seller of the option is referred to as the writer or grantor.

Types of options: Call: gives the holder the right to buy Put: gives the holder the right to sell

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An American option gives the buyer the right to exercise the option at any time between the date of writing and the expiration or maturity date.

A European option can be exercised only on its expiration date, not before.

The premium, or option price, is the cost of the option.

Basics of Options

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Basics of Options

The Philadelphia Exchange commenced trading in currency options in 1982. Currencies traded on the Philadelphia exchange:

• Australian dollar, British pound, Canadian dollar, Japanese yen, Swiss franc and the Euro.

Expiration months:• March, June, September, December plus two near-term

months.

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Basics of Options

Spot rate, 88.15 ¢/€

Size of contract:€62,500

Exercise price0.90 ¢/€

The indicated contract price is:

€62,500 $0.0125/€ = $781.25

One call option gives the holder the right to purchase €62,500 for $56,250 (= €62,500 $0.90/€)

Maturity month

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Buyer of a call:– Assume purchase of August call option on Swiss francs

with strike price of 58½ ($0.5850/SF), and a premium of $0.005/SF.

– At all spot rates below the strike price of 58.5, the purchase of the option would choose not to exercise because it would be cheaper to purchase SF on the open market.

– At all spot rates above the strike price, the option purchaser would exercise the option, purchase SF at the strike price and sell them into the market netting a profit (less the option premium).

Options Trading

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Writer of a call:

– What the holder, or buyer of an option loses, the writer gains.

– The maximum profit that the writer of the call option can make is limited to the premium.

– If the writer wrote the option naked, that is without owning the currency, the writer would now have to buy the currency at the spot and take the loss delivering at the strike price.

– The amount of such a loss is unlimited and increases as the underlying currency rises.

– Even if the writer already owns the currency, the writer will experience an opportunity loss.

Options Trading

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Buyer of a Put:– The basic terms of this example are similar to those just illustrated

with the call.

– The buyer of a put option, however, wants to be able to sell the underlying currency at the exercise price when the market price of that currency drops (not rises as in the case of the call option).

– If the spot price drops to $0.575/SF, the buyer of the put will deliver francs to the writer and receive $0.585/SF.

– At any exchange rate above the strike price of 58.5, the buyer of the put would not exercise the option, and would lose only the $0.05/SF premium.

– The buyer of a put (like the buyer of the call) can never lose more than the premium paid up front.

Options Trading

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Seller (writer) of a put:– In this case, if the spot price of francs drops below 58.5

cents per franc, the option will be exercised.

– Below a price of 58.5 cents per franc, the writer will lose more than the premium received fro writing the option (falling below break-even).

– If the spot price is above $0.585/SF, the option will not be exercised and the option writer will pocket the entire premium.

Options Trading

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An option whose exercise price is the same as the spot price of the underlying currency is said to be at-the-money (ATM).

An option the would be profitable, excluding the cost of the premium, if exercised immediately is said to be in-the-money (ITM).

An option that would not be profitable, again excluding the cost of the premium, if exercised immediately is referred to as out-of-the money (OTM).

Option Pricing & Valuation

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Call Put

Intrinsic value max(ST - X, 0) max(X - ST, 0)

in the money ST – X > 0 X – ST > 0

at the money ST – X = 0 X – ST = 0

out of the money ST – X < 0 X – ST < 0

Time Value CT – Int. value PT – Int. value

Option Pricing & Valuation

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Option Pricing & Valuation

current exchange rate (S) – as S , Call and Put strike price (X) – as X , Call and Put

time to expiration (T) – as T , both volatility of the exchange rate () – as , both

domestic interest rate (id) – as id , Call and Put

foreign interest rate (if) – as if , Call and Put

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Option Pricing & Valuation

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Forwards versus Options

-$0.90

-$0.75

-$0.60

-$0.45

-$0.30

-$0.15

$0.00

$0.15

$0.30

$0.45

$0.60

$0.75

$0.90$0

.00

$0.1

0

$0.2

0

$0.3

0

$0.4

0

$0.5

0

$0.6

0

$0.7

0

$0.8

0

$0.9

0

$1.0

0

$1.1

0

$1.2

0

$1.3

0

$1.4

0

$1.5

0

$1.6

0

$1.7

0

$1.8

0

Spot Rate at Expiration

Val

ue o

f F

orw

ard/

Put

Opt

ion

at E

xpir

atio

n

.

Value of Forward Sale at Expiration

Value of Put at Expiration

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Swaps are contractual agreements to exchange or swap a series of cash flows.

These cash flows are most commonly the interest payments associated with debt service.– If the agreement is for one party to swap its fixed

interest rate payments for the floating interest rate payments of another, it is termed an interest rate swap.

– If the agreement is to swap currencies of debt service obligation, it is termed a currency swap.

– A single swap may combine elements of both interest rate and currency swaps.

What are Swaps?

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The swap itself is not a source of capital, but rather an alteration of the cash flows associated with payment.

What is often termed the plain vanilla swap is an agreement between two parties to exchange fixed-rate for floating-rate financial obligations.

This type of swap forms the largest single financial derivative market in the world.

What are Swaps?

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There are two main reasons for using swaps:1. A corporate borrower has an existing debt service

obligation. Based on their interest rate predictions they want to swap to another exposure (e.g. change from paying fixed to paying floating).

2. Two borrowers can work together to get a lower combined borrowing cost by utilizing their comparative borrowing advantages in two different markets.

What are Swaps?

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For example, a firm with fixed-rate debt that expects interest rates to fall can change fixed-rate debt to floating-rate debt.

In this case, the firm would enter into a pay floating/receive fixed interest rate swap.

What are Swaps?

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Swap Bank

A swap bank is a generic term used to describe a financial institution that facilitates swaps between counterparties.

The swap bank serves as either a broker or a dealer. A broker matches counterparties but does not assume any of

the risk of the swap. The swap broker receives a commission for this service.

Today most swap banks serve as dealers or market makers. As a market maker, the swap bank stands willing to accept either side of a currency swap.

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Example of an Interest Rate Swap

Bank A is a AAA-rated international bank located in the U.K. that wishes to raise $10,000,000 to finance floating-rate Eurodollar loans.

Bank A is considering issuing 5-year fixed-rate Eurodollar bonds at 10 percent.

It would make more sense for the bank to issue floating-rate notes at LIBOR to finance the floating-rate Eurodollar loans.

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Example of an Interest Rate Swap

Company B is a BBB-rated U.S. company. It needs $10,000,000 to finance an investment with a five-year economic life, and it would prefer to borrow at a fixed rate. Firm B is considering issuing 5-year fixed-rate

Eurodollar bonds at 11.75 percent. Alternatively, Firm B can raise the money by issuing 5-

year floating rate notes at LIBOR + ½ percent. Firm B would prefer to borrow at a fixed rate.

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Example of an Interest Rate Swap

The borrowing opportunities of the two firms are shown in the following table.

COMPANY B BANK A DIFFERENTIAL

Fixed rate 11.75% 10% 1.75%

Floating rate LIBOR + 0.50% LIBOR 0.50%

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Example of an Interest Rate Swap

Bank A has an absolute advantage in borrowing relative to Company B

Nonetheless, Company B has a comparative advantage in borrowing floating, while Bank A has a comparative advantage in borrowing fixed.

That is, the two together can borrow more cheaply if Bank A borrows fixed, while Company B borrows floating.

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Example of an Interest Rate Swap

To see the potential advantages to a swap, imagine the two entities trying to minimize their combined borrowing costs:

COMPANY B BANK A TOGETHER

Borrow preferred method

11.75% LIBOR LIBOR + 11.75%

Borrow opposite and swap

LIBOR + 0.50% 10% LIBOR + 10.50%

POTENTIAL SAVINGS: 1.25%

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Example of an Interest Rate Swap

Now, we must determine how to split the swap savings!

If Swap Bank takes 0.25% that leaves 1% for Bank A & Company B. If they share this equally then:

- Bank A pays LIBOR - 0.5% = LIBOR – 0.5%

- Company B pays 11.75% - 0.5% = 11.25%

COMPANY B BANK A TOGETHER

Borrow preferred method

11.75% LIBOR LIBOR + 11.75%

Borrow opposite and swap

LIBOR + 0.50% 10% LIBOR + 10.50%

POTENTIAL SAVINGS: 1.25%

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Example of an Interest Rate Swap

10 3/8%

LIBOR – 1/8%

BankA

SwapBank

The swap bank makes this offer to Bank A: You pay LIBOR – 1/8 % per year on $10 million for 5 years, and we will pay you 10 3/8% on $10 million for 5 years.

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Example of an Interest Rate Swap

10 3/8%

LIBOR – 1/8%

BankA

SwapBank

Why is this swap desirable to Bank A?

10%

With the swap, Bank A pays LIBOR-1/2%

COMPANY B BANK A DIFFERENTIAL

Fixed rate 11.75% 10% 1.75%

Floating rate LIBOR + 0.50% LIBOR 0.50%

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Example of an Interest Rate Swap

LIBOR – ¼%

10 ½%

Swap

Bank

Company

B

The swap bank makes this offer to Company B: You pay us 10 ½ % per year on $10 million for 5 years, and we will pay you LIBOR – ¼ % per year on $10 million for 5 years.

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Example of an Interest Rate Swap

LIBOR – ¼%

10 ½%

Swap

Bank

Company

B

Why is this swapdesirable to Company B?

With the swap, Company B pays 11¼%

COMPANY B BANK A DIFFERENTIAL

Fixed rate 11.75% 10% 1.75%

Floating rate LIBOR + 0.50% LIBOR 0.50%

LIBOR + ½%

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Example of an Interest Rate Swap

10 3/8 %

LIBOR – 1/8% LIBOR – ¼%

10 ½%

Bank

A

Swap

Bank

Company

B

Will the swap bank make money?

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Example of an Interest Rate Swap

LIBOR + ½%

10 3/8 %

LIBOR – 1/8%LIBOR – ¼%

10 ½%

B saves ½ %

Bank

A

Swap

Bank

Company

B

A saves ½ %

The swap bank makes ¼ %

10%Note that the total savings ½ + ½ + ¼ = 1.25 % = QSD

COMPANY B BANK A DIFFERENTIAL

Fixed rate 11.75% 10% 1.75%

Floating rate LIBOR + 0.50% LIBOR 0.50%

QSD = 1.25%

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The QSD

The Quality Spread Differential (QSD) represents the potential gains from the swap that can be shared between the counterparties and the swap bank.

There is no reason to presume that the gains will be shared equally.

In the above example, Company B is less credit-worthy than Bank A, so they probably would have gotten less of the QSD, in order to compensate the swap bank for the default risk.

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Since all swap rates are derived from the yield curve in each major currency, the fixed-to-floating-rate interest rate swap existing in each currency allows firms to swap across currencies.

The usual motivation for a currency swap is to replace cash flows scheduled in an undesired currency with flows in a desired currency.

The desired currency is probably the currency in which the firm’s future operating revenues (inflows) will be generated.

Firms often raise capital in currencies in which they do not possess significant revenues or other natural cash flows (a significant reason for this being cost).

Currency Swaps

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Currency Swaps

Example: Suppose a U.S. MNC, Company A, wants to finance a £10,000,000 expansion of a British plant. They could borrow dollars in the U.S. where they are well

known and exchange dollars for pounds. This results in exchange rate risk, OR

They could borrow pounds in the international bond market, but pay a lot since they are not well known abroad.

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Example continued..

If Company A can find a British MNC with a mirror-image financing need, both companies may benefit from a swap.

If the exchange rate is S0 = 1.60 $/£, Company A needs to find a British firm wanting to finance dollar borrowing in the amount of $16,000,000.

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Example continued..

Company A is the U.S.-based MNC and Company B is a U.K.-based MNC.

Both firms wish to finance a project of the same size in each other’s country (worth £10,000,000 or $16,000,000 as S = 1.60 $/£). Their borrowing opportunities are given below.

$ £ Company A 8.0% 11.6% Company B 10.0% 12.0%

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A’s Comparative Advantage

A is the more credit-worthy of the two. A pays 2% less to borrow in dollars than B. A pays 0.4% less to borrow in pounds than B:

$ £

Company A 8.0% 11.6%

Company B 10.0% 12.0%

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B’s Comparative Advantage

B has a comparative advantage in borrowing in £. B pays 2% more to borrow in dollars than A. B pays only 0.4% more to borrow in pounds than

A: $ £

Company A 8.0% 11.6%

Company B 10.0% 12.0%

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Potential Savings = 2.0% - 0.4% = 1.6%

If Swap Bank takes 0.4% and A&B split the rest:

Company A pays 11.6% - 0.6% = 11%

Company B pays 10% - 0.6% = 9.4%

$ £

Company A 8.0% 11.6%

Company B 10.0% 12.0%

Differential (B-A) 2.0% 0.4%

Potential Savings

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Example of a Currency Swap

Company A

Swap Bank

i$=8%

i$=8%

i£=11%i£=12%

i$=9.4%

CompanyB

i£=12%

$ £

Company A 8.0% 11.6%

Company B 10.0% 12.0%

Differential (B-A) 2.0% 0.4%

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Example of a Currency Swap

Company A

Swap Bank

i$=8%

i$=8%

i£=11%i£=12%

i$=9.4%

CompanyB

i£=12%

$ £

Company A 8.0% 11.6%

Company B 10.0% 12.0%

Differential (B-A) 2.0% 0.4%

A’s net position is to borrow at i£=11%

A saves i£=0.6%

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Example of a Currency Swap

Company A

Swap Bank

i$=8%

i$=8%

i£=11%i£=12%

i$=9.4%

CompanyB

i£=12%

$ £

Company A 8.0% 11.6%

Company B 10.0% 12.0%

B’s net position is to borrow at i$=9.4%

B saves i$=0.6%

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Example of a Currency Swap

Company A

Swap Bank

i$=8%

i$=8%

i£=11%i£=12%

i$=9.4%

CompanyB

i£=12%

$ £

Company A 8.0% 11.6%

Company B 10.0% 12.0%

The swap bank makes money too:

1.4% of $16 million financed with 1% of £10

million per year for 5 years.

At S0 = 1.60 $/£, that is a gain of $64,000 per year for 5 years.

The swap bank faces exchange rate risk, but maybe they can lay it off in another swap.

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Unwinding a Swap

Discount the remaining cash flows under the swap agreement at current interest rates, and then (in the case of a currency swap) convert the target currency back to the home currency of the firm.

Payment of the net settlement of the swap terminates the swap.

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Unwinding a Swap

Suppose in the previous example, Company A wanted to unwind its (5 year) currency swap with the Swap Bank at the end of Year 3. Assume that at Year 3, the applicable dollar interest rate is 7.75% per annum, the applicable pound interest rate is 11.25% per annum, and S=1.65 $/£.

What will the net settlement amount be?

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Unwinding a Swap

There are two years of interest payments and repayment of face values remaining.

For Company A:

Paying 11% p.a. on £10,000,000

Receiving 8% p.a. on $16,000,000

Must return £10,000,000 and receive $16,000,000 at end

Net settlement for Company A is:

+ (16*0.08)/1.0775 + (16*0.08)/(1.0775)2 + 16/(1.0775)2

– [(10*0.11)/1.1125 + (10*0.11)/(1.1125)2 + 10/(1.1125)2]x1.65

= -0.358 million dollars (must pay this amount to unwind swap)