### Derivatives: Hedging against risk

**DERIVATIVE**

A product whose value is derived from the value of one or more basic variables, called bases (underlying asset, index or reference rate ), in a contractual manner. The underlying asset can be equity , forex commodity or any other asset.

**In** **the** **Indian** **context** **the** **securities** **contracts**
**(Regulation)Act, 1956(SC(R)A) defines “Derivative” to**
**include :**

•A security derived from a debt instrument ,share, loan whether secured or unsecured, risk instrument or contract for differences or any other form of security.

•A contract which derives its value from the prices, or index of prices, of underlying securities.

### Introduction (I)

In the financial marketplace some instruments are regarded as **fundamentals**,
while others are regarded as **derivatives**.

Financial Marketplace

Derivatives Fundamentals

Simply another way to catagorize the diversity in the FM*.

*Financial Market

Financial Marketplace

Derivatives Fundamentals

• Stocks

• Bonds

• Futures

• Forwards

### Introduction (II)

### What is a Derivative? (I)

Options

Swaps

Forwards Futures

**The value of the **
**derivative instrument is **

**DERIVED from the **
**underlying security**

Underlying instrument such as a commodity, a stock, a stock index, an exchange rate, a bond, another derivative etc..

Options

Swaps Forwards

Futures

The owner of an options has the **OPTION** to buy or sell
something at a predetermined price and is therefore more costly
than a futures contract.

The owner of a forward has the **OBLIGATION** to sell or buy
something in the future at a predetermined price. The difference
to a future contract is that forwards are not **standardized**.

The owner of a future has the **OBLIGATION** to sell or buy
something in the future at a predetermined price.

### What is a Derivative? (II)

A swap is an agreement between two parties to exchange a sequence of cash flows.

### Reasons to use derivatives (I)

**Hedging: **

**Speculation:**

• Interest rate volatility

• Stock price volatility

• Exchage rate volatility

• Commodity prices volatility

**VOLATILITY**

• High portion of leverage

• Huge returns

**EXTREMELY RISKY**

Derivative markets have attained an overwhelming popularity for a variety of reasons...

### Reasons to use Derivatives (II)

**Also derivatives create...**

• a **complete market**, defined as a market in which all identifiable payoffs can be
obtained by trading the securities available in the market*.

• and **market efficiency**, characterized by low transaction costs and greater
liquidity.

**Milestones in the development of Indian derivative market**

• November 18, 1996 L.C. Gupta Committee set up to draft a policy framework for introducing derivatives

• May 11, 1998 L.C. Gupta committee submits its report on the policy framework

• May 25, 2000 SEBI allows exchanges to trade in index futures

• June 12, 2000 Trading on Nifty futures commences on the NSE

• June 4, 2001 Trading for Nifty options commences on the NSE

• July 2, 2001 Trading on Stock options commences on the NSE

• November 9, 2001 Trading on Stock futures commences on the NSE

• August 29, 2008 Currency derivatives trading commences on the NSE

• August 31, 2009 Interest rate derivatives trading commences on the NSE

• February 2010 Launch of Currency Futures on additional currency pairs

•

**Difference between forwards and futures**

**Forwards ** **Futures**

Two parties Three Parties

Autonomous Regulated

Privately negotiated contracts Traded on an exchange Not standardized Standardized contracts Settlement dates can be Fixed settlement dates as set by the parties declared by the exchange High counter party risk Almost no counter party risk

### Derivatives in India (1)

### • Sodhani Committee (expert group on

### foreign exchange) was formed in 1992 to look into the issues in and development of the foreign exchange market in India

### • Some recommendations

– Corporates should be allowed to hedge upon declaration of underlying assets

– Banks may be permitted to initiate overseas

### Sodhani Committee..

• Banks should be allowed to borrow and lend in the overseas markets

• More participants be allowed in the foreign exchange market

• Corporates must be allowed to cancel and re- book option contracts

• Banks be permitted to use hedging instruments for their own ALM

• Banks to be allowed to fix interest rates on

FCNR (B) deposits subject to caps fixed by RBI

### Derivatives in India (2)

• The use of financial derivatives started in India is the nineties’ in the foreign exchange and stock market

• In 1992 RBI had permitted banks to offer cross currency options to their clients

• In 1996 banks were allowed to offer their

corporate clients interest rate swaps, currency swaps, interest rate options and forward rate agreements

• The derivatives market in India is still in an

### Milestones in the development of Indian derivative market

◼ November 18, 1996 L.C. Gupta Committee set up to draft a policy

framework for introducing derivatives

◼ May 11, 1998 L.C. Gupta committee submits its report on the policy

framework

◼ May 25, 2000 SEBI allows exchanges to trade in index futures

◼ June 12, 2000 Trading on Nifty futures commences on the NSE

◼ June 4, 2001 Trading for Nifty options commences on the NSE

◼ July 2, 2001 Trading on Stock options commences on the NSE

◼ November 9, 2001 Trading on Stock futures commences on the NSE

### Conti…

◼ August 29, 2008 Currency derivatives trading commences on the NSE

◼ August 31, 2009 Interest rate derivatives trading commences on the NSE

◼ February 2010 Launch of Currency Futures on additional currency pairs

◼ October 28, 2010 Introduction of European style Stock Options

### Options (I)

Options The owner of an options has the OPTION to buy or sell something at a predetermined price and is therefore more costly than a futures.

**Some terms to understand: **

• Call option

• Put option

• Excersice price / strike price

• Option premium

• Moneyness (in-the-money, at-the-money, out-of-money)

• European vs. American Options

**Factors impacting option prices**

### Options (II)

Call Option

Write Purchase

Write
**The four basic positions: **

### Payoff (at time of expiration) for a Call option

0

Break-even Exercise price (X)

Spot Price

Premium paid Payoff of

option

### Payoff (at time of expiration) for a Put option

0

Exercise price (X)

Spot Price Payoff of

option

An investor buys one European Call option on one share of Neyveli Lignite at a premium of Rs.2 per share on 31 July.

The strike price is Rs.60 and the contract matures on 30 September. It may be clear form the graph that even in the worst case scenario, the investor would only lose a maximum of Rs.2 per share which he/she had paid for the premium. The upside to it has an unlimited profits

opportunity.

On the other hand the seller of the call option has a payoff chart completely reverse of the call options buyer. The maximum loss that he can have is unlimited though a profit of Rs.2 per share would be made on the premium payment by the buyer.

**Illustration on Call Option**

### Options (VI)

**Write & Purchase Call Option: **

Profit and Loss

Stock Price at Expiration

Long Put

Premium Earned

An investor buys one European Put Option on one share of Neyveli Lignite at a premium of Rs. 2 per share on 31 July. The strike price is Rs.60 and the contract matures on 30 September. The adjoining graph shows the fluctuations of net profit with a

**Illustration on Put Options**

### The Black-Scholes-Merton Option Pricing Model

• The Black-Scholes-Merton option pricing model says the value of a stock option is determined by six factors:

*S, the current price of the underlying stock*

*y, the dividend yield of the underlying stock*

*K, the strike price specified in the option contract*

*r, the risk-free interest rate over the life of the option contract*

*T, the time remaining until the option contract expires*

, (sigma) which is the price volatility of the underlying stock

15-42

### The Black-Scholes-Merton Option Pricing Formula

• The price of a call option on a single share of common
stock is: C = Se^{–yT}*N(d*_{1}*) – Ke*^{–rT}*N(d*_{2}*)*

• The price of a put option on a single share of common
stock is: P = Ke^{–rT}*N(–d*_{2}*) – Se*^{–yT}*N(–d*_{1}*)*

### ( ) ( )

**σ** **T**
**d**

**d**

**σ** **T**

**T**
**σ** **2**

**y**
**r**

**K**
**S**
**d** **ln**

**1**
**2**

**2**
**1**

−

=

+

−

=

d_{1} and d_{2} are calculated using these two formulas:

### Formula Details

• In the Black-Scholes-Merton formula, three common fuctions are used to price call and put option prices:

– e^{-rt}, or exp(-rt), is the natural exponent of the value of –rt (in
common terms, it is a discount factor)

– ln(S/K) is the natural log of the "moneyness" term, S/K.

– N(d1) and N(d2) denotes the standard normal probability for the values of d1 and d2.

• In addition, the formula makes use of the fact that:

N(-d_{1}) = 1 - N(d_{1})

15-44

### Example: Computing Prices for Call and Put Options

• Suppose you are given the following inputs:

S = $50 y = 2%

K = $45

T = 3 months (or 0.25 years)

= 25% (stock volatility) r = 6%

• What is the price of a call option and a put option, using the Black-Scholes-Merton option pricing formula?

### We Begin by Calculating d

_{1}

### and d

_{2}

( ) ( ) ^{(} ^{)} ( )

**0.86038**
**0.25**

**0.25**
**0.98538**

**σ** **T**
**d**
**d**

**0.98538**
** **

** **
** **

** **
** **

**0.125**

**0.25**
**0.07125**

**0.10536**
** **

** **
** **

** **
** **

**0.25**
**0.25**

**0.25**
**2**

**0.25**
**0.02**

**0.06**
**45**

**50**
**ln**
**σ** **T**

**T**
**σ** **2**

**y**
**r**
**K**
**S**
**d** **ln**

**1**
**2**

**2**
**2**

**1**

=

−

=

−

=

=

= +

+

−

= +

−

=

Now, we must compute N(d_{1}) and N(d_{2}). That is, the
**standard normal probabilities.**

15-46

### Calculating Delta

• * Delta* measures the dollar impact of a change in the
underlying stock price on the value of a stock option.

*Call option delta* *= e*^{–yT}*N(d*_{1}*) > 0*
*Put option delta* = –e^{–yT}*N(–d*_{1}*)* < 0

• A $1 change in the stock price causes an option price to change by approximately delta dollars.

### Example: Calculating Delta

**Stock Price:** **50.00** **Discounted Stock:** **49.75**
**Strike Price:** **45.00** **Discounted Strike:** **44.33**
**Volatility (%):** **25.00**

**Time (in years):** **0.2500**
**Riskless Rate (%):** **6.00**
**Dividend Yield (%):** **2.00**

**d(1):** **0.98538**

**N(d1):** **0.83778** **N(-d1):** **0.16222**

**Call Delta:** **0.83360**

**d(2):** **0.86038**

**N(d2):** **0.80521** **N(-d2):** **0.19479**

**Put Delta:** **-0.16141**

**Call Price:** **$ ****5.985**
**Put Price:** **$ ****0.565**

15-48

### Calculating Vega

• *Vega* measures the impact of a change in stock price
volatility on the value of stock options.

• Vega is the same for both call and put options.

*Vega* = Se^{–yT}*n(d*_{1}*)T* > 0

*n(d)* represents a standard normal density, e^{-d/2}/ 2p

• If the stock price volatility changes by 100% (i.e., from 25% to 125%), option prices increase by about vega.

### Example: Calculating Vega

**Stock Price:** **50.00** **Discounted Stock:** **49.75**
**Strike Price:** **45.00** **Discounted Strike:** **44.33**
**Volatility (%):** **25.00**

**Time (in years):** **0.2500**
**Riskless Rate (%):** **6.00**
**Dividend Yield (%):** **2.00**

**d(1):** **0.98538**

**N(d1):** **0.83778** **N(-d1):** **0.16222**

**Call Delta:** **0.83360** **n(d1):** **0.24375**

**d(2):** **0.86038**

**N(d2):** **0.80521** **N(-d2):** **0.19479**

**Put Delta:** **-0.19382**

**Call Price:** **$ ****5.985**

**Vega:** **6.06325**

**Put Price:** **$ ****0.565**

15-50

### The "Vega" Prediction:

• The vega value of 6.063 predicts that if the stock price volatility increases by 100% (i.e., from 25% to 125%), call and put option prices will increase by $6.063.

• Generally, traders divide vega by 100—that way the prediction is: if the stock price volatility increases by 1% (25% to 26%), call and put option prices will both increase by about $0.063.

• If stock price volatility increases from 25% to 26%, you can use the spreadsheet to see that the

– Call option price is now $6.047, an increase of $0.062.

– Put option price is now $0.627, an increase of $0.062.

### Other Impacts on Option Prices from Input Changes

• * Gamma* measures delta sensitivity to a stock price change.

– A $1 stock price change causes delta to change by approximately the amount gamma.

• * Theta* measures option price sensitivity to a change in time
remaining until option expiration.

– A one-day change causes the option price to change by approximately the amount theta.

• * Rho* measures option price sensitivity to a change in the interest
rate.

– A 1% interest rate change causes the option price to change by approximately the amount rho.

15-52

### Chapter Review, I.

• The Black-Scholes-Merton Option Pricing Model

• Valuing Employee Stock Options

• Varying the Option Price Input Values

– Varying the Underlying Stock Price – Varying the Option’s Strike Price

– Varying the Time Remaining until Option Expiration – Varying the Volatility of the Stock Price

– Varying the Interest Rate – Varying the Dividend Yield

### Chapter Review, II.

• Measuring the Impact of Input Changes on Option Prices

– Interpreting Option Deltas – Interpreting Option Etas – Interpreting Option Vegas

– Interpreting an Option’s Gamma, Theta, and Rho

• Implied Standard Deviations

• Hedging a Stock Portfolio with Stock Index Options

• Implied Volatility Skews

A futures contract is an agreement between two parties to buy or sell an asset at a certain time in the future at a certain price. Futures contracts are special

types of forward contracts in the sense that the former are standardized

exchange-traded contracts, such as futures of the Nifty index.

**Economic Importance of ** **the Futures Market**

**•** **Price Discovery - Due to its highly**
**competitive nature, the futures market has**
**become an important economic tool to**
**determine prices based on today's and**
**tomorrow's estimated amount of supply**

**Risk Reduction** - Futures markets are also a place
for people to reduce risk when making
purchases. Risks are reduced because the price
is pre-set, therefore letting participants know how
much they will need to buy or sell. This helps
reduce the ultimate cost to the retail buyer
because with less risk there is less of a
chance that manufacturers will jack up prices to
make up for profit losses in the cash market.

Background

◦ 1972: Chicago Mercantile Exchange opens International Monetary Market. (IMM)

◦ IMM provides an outlet for hedging currency risk with futures contracts

Futures Contracts: contracts written requiring a

Advantages of Futures

Smaller contract size

Easy liquidation

Well-organized and stable market.

Little default risk.

Disadvantages of Futures

Currencies available limited

Limited dates of delivery

Rigid contract sizes.

### Future mechanism

**Differences between futures and options**

**Future** **Options**

Both the buyer and the seller are under an obligation to fulfill the contract.

The buyer of the option has the right and not an obligation whereas the seller is under obligation to fulfill the contract if and when the buyer exercises his right.

The buyer and the seller are subject to unlimited risk of loss.

The seller is subjected to unlimited risk of losing whereas the buyer has limited potential to lose (which is the option premium).

The buyer and the seller have

potential to make unlimited gain or loss.

The buyer has potential to make unlimited gain while the seller has a

potential to make unlimited gain. On the other hand the buyer has a limited loss

**Payoff for futures**

### Futures contracts have linear payoffs. In

### Simple words, it means that the losses as

### well as profits for the buyer and the seller

### of a futures contract are unlimited. These

### linear Payoffs are fascinating as they can

### be combined with options and the

### underlying to generate various complex

**A payoff is the likely profit/loss that would**
**accrue to a market participant with change in**
**the**

**price** **of** **the** **underlying** **asset.** **This** **is**
**generally depicted in the form of payoff**
**diagrams which**

**show the price of the underlying asset on the**
**X–axis and the profits/losses on the Y–axis.**

**In this**

**section we shall take a look at the payoffs for**
**buyers and sellers of futures and options.**

### 1.

The stock of the an investor has gone downfrom Rs.450 to Rs. 400 and further it is likely to go down.

### 2.

He should take a short futures position.### 3.

2 months future cost him Rs. 415 for that he has to keep the margin money.### 4.

If price goes down to Rs. 360, he is looser by Rs. 40 per share.### 5.

But his short position will start making profit.### Hedging: Long security, sell futures

### Payoff for a buyer of Nifty futures

The figure shows the profits/losses for a long futures

position. The investor bought futures when the index was at 6200.

Profit

0 6200 Nifty

Loss

### Payoff for a seller of Nifty futures

The figure shows the profits/losses for a short futures position. The investor sold futures when the index was at

4000

### .

Profit

0 4000

Loss

If the index goes down, his futures position starts making

### ACCOUNTING AND TAX

### ▪ **Accounting** Consider a trader who in September 2002 takes a long position in a March 2003 corn futures contract and closes out the position at the end of February 2003.

**Accounting**

### ▪ Suppose that the futures prices are 150 cents

### per bushel when the contract is entered into,

### 170 cents per bushel at the end of 2002, and

### 180 cents per bushel when the contract is

### closed out. One contract is for the delivery of

### 5,000 bushels. If the trader is a speculator, the

### gains for accounting purposes are

### Currency and Interest Rate Swaps

**Chapter Objective:**

This chapter discusses currency and interest rate swaps, which are relatively new instruments for hedging long- term interest rate risk and foreign exchange risk.

**Chapter Outline:**

• Types of Swaps

• Size of the Swap Market

• The Swap Bank

• Interest Rate Swaps

Swaps A swap is an agreement between two parties to exchange a sequence of cash flows.

### Swaps (I)

• Counterparties

• Interest rate swaps

• Currency swaps

• Phenomenal growth of the swap market

• Future and Option markets only provide for short term investment horizon

• Traded in OTC markets with little regulations

• No secondary market

• Market limited to institutional investors

**6.75**

**Swaps**

• **Contracts that can be constructed with **
**multiple forward contracts**

• An agreement to exchange cash flows at specified
* future times* according to certain specified rules

• **Types of swaps**

– **Interest Rate Swaps**
– **Currency Swaps**

– **Commodity Swaps**

### Swap Market

In a swap, two counterparties agree to a contractual

arrangement wherein they agree to exchange cash flows at periodic intervals.

There are two basic types of swaps:

◼ Single Currency Interest rate swap

⚫ “Plain vanilla” fixed-for-floating swaps in one currency.

◼ Cross Currency Interest Rate Swap (Currency swap)

⚫ Fixed for fixed rate debt service in two (or more) currencies.

The most popular currencies are: US$, Yen, Euro, SF, BP

**6.77**

**Plain Vanilla Interest Rate Swap **

**Firm A pays 5% fixed and receives LIBOR**

**Firm A** **Swap **

**Dealer**

Pay 5%

Receive 6 mo. LIBOR

If the swap is being used by Firm A as a hedge, what

**6.78**

**Typical Uses of an** **Interest Rate Swap**

### • Converting a liability from

### – fixed rate to floating rate – floating rate to

### fixed rate

### • Converting an investment from

### – fixed rate to floating rate

### – floating rate to fixed

### rate

**6.79**

**Valuation of an Interest Rate ** **Swap**

### • Interest rate swaps can be valued as the difference between the value of a fixed- rate bond and the value of a floating-rate bond

### • Alternatively, they can be valued as a

### portfolio of forward rate agreements

**6.80**

**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

**6.81**

**Valuation in Terms of FRAs**

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

### • The FRAs can be valued on the assumption

**6.82**

**Valuation of an Interest Rate ** **Swap: an Example**

• Suppose that, under the terms of a swap, a

financial institution has agreed to pay six-month LIBOR and receive 8% per annum (with

semiannual compounding) on a notional principal of $100 million. The swap has a remaining life of 1.25 years. The LIBOR rates with continuous

compounding for 3-month, 9-month and 15-month maturities are 10%, 10.5%, and 11%, respectively.

The 6-month LIBOR at the last payment date was 10.2% (with semiannual compounding).

**6.83**

**Currency Swap**

### • Example : A bilateral agreement to

- *Receive* 8% on a US$ principal of 15,000,000
- and Pay 11% on a sterling principal of

$10,000,000

- cash flows are exchanged every year for 5 years

### • Principal is exchanged at the beginning and

**6.84**

**Fixed-for-fixed Currency Swap**

Years

Dollars Pounds

$

---millions--- 0 –15.00 +10.00 1 +1.20 –1.10

2 +1.20 –1.10 3 +1.20 –1.10 4 +1.20 –1.10 5 +16.20 -11.10

£

**6.85**

**Typical Uses of a ** **Currency Swap**

### • Conversion from a liability in one

### currency to a

### liability in another

### • Conversion from

### an investment in

### one currency to an

### investment in

**6.86**

**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

**6.87**

**Valuation of a Currency Swap: an ** **Example**

• Suppose that the term structure of interest rates is flat in both Japan and the US. The Japanese

interest rate is 4% per annum and the US rate is 9% per annum (both with continuous

compounding). A financial institution has entered into a currency swap in which it receives 5% per annum in yen and pays 8% per annum in dollars once a year. The principals in the two currencies are $10 million and 1,200 million yen. The swap will last for another three years, and the current

**6.88**

**Commodity Swaps: Oil Swap**

• In 1986, the first oil swap was intermediated by Chase Manhattan Bank

• The parties agree on a notional amount that is expressed in barrels of oil (rather than in dollars)

• Similar to a fixed-for-floating interest rate swap,

payments are made on the basis of fixed and floating oil prices.

– * Example:* One party receives a cash flow based on an oil
price that is fixed at the origination of the contract and pays
a cash flow based on the average spot price over a period.

• Oil prices increase, this party makes a net payment

• Oil prices decrease, this party receives a net payment

• No physical quantities of oil are exchanged.

**Swaps & Forwards**

**6.89**

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

• The “plain vanilla” interest rate swap in our example consisted of 6 FRAs

• The “fixed for fixed” currency swap in our example consisted of a cash transaction & 5 forward contracts

• The value of the swap is the sum of the values of the forward contracts underlying the swap

• Swaps are normally “at the money” initially

– This means that it costs nothing to enter into a swap

– It does not mean that each forward contract underlying

**6.90**

**Credit Risk**

### • A swap is worth zero to a company initially

### • At a future time its value is liable to be either positive or negative

### • The company has credit risk exposure only

### when its value is positive

### The Swap Bank

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

The swap bank can serve as either a broker or a dealer.

◼ As a broker, the swap bank matches counterparties but does not assume any of the risks of the swap.

◼ As a dealer, the swap bank stands ready to accept either

### Interest Rate Swap

Used by companies and banks that require either fixed or floating-rate debt.

Interest rate swaps allow the companies (or banks) and the swap bank to benefit by swapping fixed-for-floating interest payments.

Since principal is in the same currency and the same amount, only interest payments are exchanged (net).

### Interest Rate Swap

Each party will issue the less advantageous form of debt.

Swap Bank Company A

prefers floating

Company B prefers fixed

Pay fixed Pay floating

Receive Floating Receive

fixed

### An Example of an Interest Rate Swap

**Bank A** is a AAA-rated international bank located in the UK and wishes to
raise $10M to finance floating-rate Eurodollar loans.

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

◼ Bank A can issue 5-year fixed-rate Eurodollar bonds at 10 %

**Firm B** is a BBB-rated U.S. company. It needs $10 M to finance an investment
with a five-year economic life.

◼ Firm B can issue 5-year fixed-rate Eurodollar bonds at 11.75 %

◼ Alternatively, firm B can raise the money by issuing 5-year floating-rate notes at LIBOR + 0.50 percent.

◼ Firm B would prefer to borrow at a fixed rate because it locks in a financing cost.

The borrowing opportunities

of the two firms are: **COMPANY B ****BANK A **

* Fixed rate * 11.75% 10%

* Floating rate * LIBOR + .5% LIBOR

### The Quality Spread Differential

**QSD** represents the potential gains from the swap that can be
shared between the counterparties and the swap bank.

QSD arises because of a difference in default risk premiums for fixed (usually larger) and floating rate (usually smaller) instruments for parties with different credit ratings

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

equally, usually the company with the higher credit rating will take more of the QSD.

In the above example, company B is less credit-worthy than

### An Example of an Interest Rate Swap

The swap bank makes this offer to Bank A: You pay LIBOR per year on $10 million for 5 years and we will pay you 10.50% on $10

million for 5 years

**COMPANY B ****BANK A **

* Fixed rate * 11.75% 10%

* Floating rate * LIBOR + .5% LIBOR

**Swap**
**Bank**

**LIBOR**
**10.50%**

**Bank**
**A**

Issue $10M debt at 10% fixed-rate

**COMPANY B ****BANK A **

* Fixed rate * 11.75% 10%

### An Example of an Interest Rate Swap

Here’s what’s in it for Bank A:

Bank A can borrow externally at 10% fixed and have a net borrowing position of

-10.50% + 10% + LIBOR = LIBOR – 0.50% which is 0.50

% better than they can borrow floating without a swap.

**10%**

0.50% of $10,000,000

= $50,000. That’s quite a cost savings per year for 5 years.

**Swap**
**Bank**

**LIBOR **
**10.50%**

**Bank**
**A**

### An Example of an Interest Rate Swap

**Company **
**B**

The swap bank makes this offer to company B:

You pay us 10.75% per year on $10 million for 5 years and we will pay you LIBOR per year on

$10 million for 5 years.

**Swap**
**Bank**

**10.75%**

**LIBOR **

**COMPANY B ****BANK A **

* Fixed rate * 11.75% 10%

* Floating rate * LIBOR + .5% LIBOR

Issue $10M debt at

LIBOR+0.50% floating-rate

**COMPANY B ****BANK A **

* Fixed rate * 11.75% 10%

### An Example of an Interest Rate Swap

Firm B can borrow externally at LIBOR + .50 % and have a net borrowing position of

10.75 + (LIBOR + .50 ) - LIBOR = 11.25% which is 0.50 % better than they can borrow floating

(11.75%).

**LIBOR **
**+ .50%**

Here’s what’s in it for Firm B:

0.5 % of $10,000,000 =

$50,000 that’s quite a cost savings per year for 5 years.

**Swap**
**Bank**

**Company **
**B**

**10.75%**

**LIBOR **

### An Example of an Interest Rate Swap

The swap bank makes money too.

.25% of $10 million =

$25,000 per year for 5 years.

LIBOR+10.75%– LIBOR-10.50%=0.25%

**Swap**
**Bank**

**Company **
**B**

**10.75%**

**LIBOR**
**LIBOR**

**10.50%**

**Bank**
**A**

**COMPANY B ****BANK A **

* Fixed rate * 11.75% 10%

* Floating rate * LIBOR + .5% LIBOR

### An Example of an Interest Rate Swap

**Swap**
**Bank**

**Company **
**B**

**10.75%**

**LIBOR**
**LIBOR**

**10.50%**

**Bank**
**A**

**B saves .50%**

**A saves .50%**

**The swap bank makes .25%**

**COMPANY B ****BANK A **

* Fixed rate * 11.75% 10%

### Example: Interest Rate Swap

◼ Company A can borrow at 8% fixed or LIBOR + 1% floating (borrows fixed)

◼ Company B can borrow at 9.5% fixed or LIBOR + .5% (borrows floating)

◼ Company A prefers floating and Company B prefers fixed

◼ By entering into the swap agreements, both A and B are better off then they would be borrowing from the bank and the swap dealer makes .5%

Pay Receive Net

Company A LIBOR 8% ^{-}

(LIBOR+.25)

Swap Dealer w/A 7.75% LIBOR

Company B 8.25% LIBOR -8.75%

Swap Dealer w/B LIBOR 8.5%

Swap Dealer Net LIBOR+7.75

%

LIBOR+8.25% +0.50%

### Currency Swaps

Most often used when companies make cross- border capital investments or projects.

◼ Ex., U.S. parent company wants to finance a project undertaken by its subsidiary in Germany. Project proceeds would be used to pay interest and principal.

◼ Options:

1. Borrow US$ and convert to Euro – exposes company to exchange rate risk.

2. Borrow in Germany – rate available may not be as good as that in

### Currency Swaps

Typically, a company should have a comparative
**advantage in borrowing locally**

issue local issue local

Swap Bank Company

A

Company B

Pay foreign pay foreign

Receive local

Receive local

Issue local Issue local

### An Example of a Currency Swap

Suppose a U.S. MNC wants to finance a €40,000,000 expansion of a German plant.

They could borrow dollars in the U.S. where they are well known and exchange for dollars for euros.

◼ This will give them exchange rate risk: financing a euro project with dollars.

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

If they can find a German MNC with a mirror-image financing need they may both benefit from a swap.

If the spot exchange rate is S_{0}($/ €) = $1.30/ €, the U.S. firm

### An Example of a Currency Swap

Consider two firms A and B: firm A is a U.S.–based multinational and firm B is a Germany–based multinational.

Both firms wish to finance a project in each other’s country of the same size. Their borrowing opportunities are given in the table below.

**$ ****€ **

* Company A * 8.0% 7.0%

* Company B * 9.0% 6.0%

**$8%**

### An Example of a Currency Swap

**Firm **
**B**

**$8%** **€ 6%**

**Swap**
**Bank**

**Firm**
**A**

**€ 6%**

**$8%**

**€ 6%**

**$ ****€ **

* Company A * 8.0% 7.0%

**Borrow**

**$52M** **Borrow**

**€ 40M**
**Annual **

**Interest**

**$4.16M**

**Annual **
**Interest**

**€2.4 M**

**Annual **
**Interest**

**$4.16M**

**Annual **
**Interest**

**€2.4 M**

**$8%**

### An Example of a Currency Swap

**Firm **
**B**

**$8%** **€ 6%**

**Swap**
**Bank**

**Firm**
**A**

**€ 6%**

**$8%**

**€ 6%**

**$ ****€ **

* Company A * 8.0% 7.0%

* Company B * 9.0% 6.0%

**$52M** **€ 40M**

**A’s net position is to **
**borrow at € 6%**

**B’s net position is to **
**borrow at $8%**

### Swap Market Quotations

Swap banks will tailor the terms of interest rate and currency swaps to

customers’ needs. They also make a market in “plain vanilla” and currency swaps and provide quotes for these. Since the swap banks are dealers for these swaps, there is a bid-ask spread.

**Interest Rate Swap Example:**

Swap bank terms: USD: 2.50 – 2.65

Means that the bank is willing to pay fixed-rate 2.50% interest against receiving LIBOR OR bank is willing to receive fixed-rate 2.65% against paying LIBOR.

**Currency Swap Example:**

Swap bank terms: USD 2.50 – 2.65

Euro 3.25 – 3.50

Means that bank is willing to make fixed rate USD payments at 2.5% in return for receiving fixed rate Euro at 3.5% OR the bank is willing to

### Risks of Interest Rate and Currency Swaps

**Interest Rate Risk**

Interest rates might move against the swap bank after it has only gotten half of a swap on the books, or if it has an unhedged position.

**Basis Risk **

Floating rates of the two counterparties being pegged to two different indices
**Exchange rate Risk**

Exchange rates might move against the swap bank after it has only gotten half of a swap set up.

**Credit Risk**

This is the major risk faced by a swap dealer—the risk that a counter party will default on its end of the swap.

**Mismatch Risk**

It’s hard to find a counterparty that wants to borrow the right amount of money for the right amount of time.

**Sovereign Risk**

The risk that a country will impose exchange rate restrictions that will interfere with performance on the swap.

**INTERNATIONAL** **FINANCIAL** **MANAGEMENT**

EUN / RESNICK Fifth Edition

### Chapter Objective:

### This chapter discusses currency and interest rate swaps, which are relatively new instruments for hedging long-term interest rate risk and foreign exchange risk.

## 14

Chapter Fourteen

### Interest Rate and Currency Swaps

**14-112**

**Chapter Outline**

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

⚫ Types of Swaps

⚫ Size of the Swap Market

⚫ The Swap Bank

⚫ Swap Market Quotations

⚫ Interest Rate Swaps

⚫ Currency Swaps

⚫ Variations of Basic Interest Rate and Currency Swaps

⚫ Risks of Interest Rate and Currency Swaps

⚫ Is the Swap Market Efficient?

**Definitions**

⚫

### In a swap, two counterparties agree to a

### contractual arrangement wherein they agree to exchange cash flows at periodic intervals.

⚫

### There are two types of interest rate swaps:

⚫ Single currency interest rate swap

⚫ “Plain vanilla” fixed-for-floating swaps are often just called
*interest rate swaps.*

⚫ Cross-Currency interest rate swap

⚫ This is often called a currency swap; fixed for fixed rate debt service in two (or more) currencies.

**14-114**

**Size of the Swap Market**

⚫

### In 2007 the notational principal of:

Interest rate swaps was $271.9 trillion USD.

Currency swaps was $12 trillion USD

⚫

### The most popular currencies are:

⚫ U.S. dollar

⚫ Japanese yen

⚫ Euro

⚫ Swiss franc

⚫ British pound sterling

**The Swap Bank**

⚫

### A swap bank is a generic term to describe a financial institution that facilitates swaps

### between counterparties.

⚫

### The swap bank can serve as either a broker or a dealer.

⚫ As a broker, the swap bank matches counterparties but does not assume any of the risks of the swap.

⚫ As a dealer, the swap bank stands ready to accept either side of a currency swap, and then later lay off their risk, or match it with a counterparty.

**14-116**

**Swap Market Quotations**

⚫

### Swap banks will tailor the terms of interest rate and currency swaps to customers’ needs

⚫