Chapter 13 Financial Derivatives © 2005 Pearson Education Canada Inc

Chapter 13

Financial Derivatives

© 2005 Pearson Education Canada Inc.

© 2005 Pearson Education Canada Inc. 13-2

Hedging

Hedge: engage in a financial transaction that reduces or eliminates risk

Basic hedging principle:Hedging risk involves engaging in a financial transaction that offsets a long position by taking a short position, or offsets a short position by taking a additional long position


Buying and Writing Calls

• A call option is an option that gives the owner the right (but not the obligation) to buy an asset at a pre specified exercise (or striking) price within a specified period of time.

• Since a call represents an option to buy, the purchase of a call is undertaken if the price of the underlying asset is expected to go up.

• The buyer of a call is said to be long in a call and the writer is said to be short in a call.

• The buyer of a call will have to pay a premium (called call premium) in order to get the writer to sign the contract and assume the risk.


The Payoff from Buying a Call

To understand calls, let's assume that you hold a European call on an asset with an exercise price of X and a call premium of α.

• If at the expiration date, the price of the underlying asset, S, is less than X, the call will not be exercised, resulting in a loss of the premium.

• At a price above X, the call will be exercised. In particular, at a price between X and X + α, the gain would be insufficient to cover the cost of the premium, while at a price above X + α the call will yield a net profit.

• In fact, at a price above X + α, each $1 rise in the price of the asset will cause the profit of the call option to increase by $1.


The Payoff from Writing a Call

The payoff function from writing the call option is the mirror image of the payoff function from buying the call.

Note that the writer of the call receives the call premium, α, up front and must stand ready to sell the underlying asset to the buyer of the call at the exercise price, X, if the buyer exercises the option to buy.


Summary and Generalization

In general, the value of a call option, C, at expiration with asset price S (at that time) and exercise price X is

C = max (0, S - X)

In other words, the value of a call option at maturity is S - X, or zero, whichever is greater.

• If S > X, the call is said to be in the money, and the owner will exercise it for a net profit of C - α.

• If S < X, the call is said to be out of the money and will expire worthless.

• A call with S = X is said to be at the money (or trading at par).


Buying and Writing Puts

A second type of option contract is the put option. It gives the owner the right (but not the obligation) to sell an asset to the option writer at a pre specified exercise price.

• As a put represents an option to sell rather than buy, it is worth buying a put when the price of the underlying asset is expected to fall.

• As with calls, the owner of a put is said to be long in a put and the writer of a put is said to be short in a put.

• Also, as with calls, the buyer of a put option will have to pay a premium (called the put premium) in order to get the writer to sign the contract and assume the risk.


The Payoff from Buying a Put

Consider a put with an exercise price of X and a premium of β.

• At a price of X or higher, the put will not be exercised, resulting in a loss of the premium.

• At a price below X - β, the put will yield a net profit.

• In fact, between X - β and X, the put will be exercised, but the gain is insufficient to cover the cost of the premium.


The Payoff from Writing a Put

The payoff function from writing a put is the mirror image of that from buying a put.

As with writing a call, the writer of a put receives the put premium, β, up front and must sell the asset underlying the option if the buyer of the put exercises the option to sell.


Summary and Generalization

In general, the value of a put option, P, at the expiration date with exercise price X and asset price S (at that time) is

P = max (X - S, 0)

That is, the value of a put at maturity is the difference between the exercise price of the option and the price of the asset underlying the option, X - S, or zero, whichever is greater.

• If S > X, the put is said to be out of the money and will expire worthless.

• If S < X, the put is said to be in the money and the owner will exercise it for a net profit of P - β.

• If S = X, the put is said to be at the money.


Factors Affecting Premium

1. Higher strike price lower premium on call options and higher premium on put options

2. Greater term to expiration higher premiums for both call and put options

3. Greater price volatility of underlying instrument higher premiums for both call and put options


Spot, Forward, and Futures Contracts

• A spot contract is an agreement (at time 0) when the seller agrees to deliver an asset and the buyer agrees to pay for the asset immediately (now)

• A forward contract is an agreement (at time 0) between a buyer and a seller that an asset will be exchanged for cash at some later date at a price agreed upon now

• A futures contract is similar to a forward contract and is normally arranged through an organized exchange (i.e., ME, CBT)The main difference between a futures and a forward contract is that the price of a forward contract is fixed over the life of the contract, whereas futures contracts are marked-to-market daily.


Financial Futures Markets

Financial futures are classified as

• Interest-rate futures

• Stock index futures, and

• Currency futures

In Canada, financial futures are traded in the Montreal Exchange (see Table 13-1)


Interest-Rate Forward MarketsLong position = agree to buy securities at future dateHedges by locking in future interest rate if funds coming in futureShort position = agree to sell securities at future dateHedges by reducing price risk from change in interest rates if

holding bondsPros1. Flexible (can be used to hedge completely the interest rate risk)Cons1. Lack of liquidity: hard to find a counterparty to make a

contract with2. Subject to default risk: requires information to screen good

from bad risk


Widely Traded Interest-RateFutures Contracts


Interest Rate Futures Markets

Interest Rate Futures Contract1. Specifies delivery of type of security at future date2. Arbitrage at expiration date, price of contract = price of the

underlying asset delivered3. i , long contract has loss, short contract has profit4. Hedging similar to forwards

Micro vs. macro hedge

Traded on Exchanges: Global competition

Success of Futures Over Forwards1. Futures more liquid: standardized, can be traded again, delivery of

range of securities2. Delivery of range of securities prevents corner3. Mark to market: avoids default risk4. Don’t have to deliver: netting


Widely Traded Stock Index Futures Contracts


Widely Traded Currency Futures

13-19

Profits and Losses: Options vs. Futures

$100,000 Canada-bond contract,1. Exercise price of 115,

$115,000.2. Premium = $2,000

© 2005 Pearson Education Canada Inc.


Payoff Function from Buying an Interest Rate Futures (see Fig. 13-1)

Consider the June Canada bond futures contract traded on the ME. If you buy this contract for 115, you agree to pay $115,000 for $100,000 face value of long-term Canadas when they are delivered to you at the end of June. If at the expiration date the underlying Canada bond for the futures contract has a price of

• 110, meaning that the price of the futures contract also falls to 110, you suffer a loss of 5 points, or $5,000 (point A')

• 115, you would have a zero profit (point B')

• 120, you would have a profit on the contract of 5 points, or $5,000 (point C')


Payoff Function from Selling an Interest Rate Futures (see Fig. 13-1)

If you sell this contract for 115, you agree to deliver $100,000 face value of long-term Canada bonds for $115,000 at the end of June. If at the expiration date the underlying Canada bond for the futures contract has a price of

• 110, meaning that the price of the futures contract also falls to 110, you gain 5 points, or $5,000 (point A')

• 115, you would have a zero profit (point B')

• 120, you would have a loss on the contract of 5 points, or $5,000 (point C')


Figure 13-1. Interest Rate Futures Options

An option contract on the ME's June Canada bond futures contract has the following key features:

• it has the same expiration date as the underlying futures contract

• it is an American option and so can be exercised at any time before the expiration date, and

• the premium of the option is quoted in points that are the same as in the futures contract, so each point corresponds to $1,000.


How Interest Rate Futures Options Work (see Fig. 13-1)

Suppose that today you buy, for a $2,000 premium, a European call on the $100,000 June Canada bond futures contract with a strike price of 115. If at the expiration date the underlying Canada bond for the futures contract has a price of

• 110, the futures call will be out of the money, since S<X. It will expire worthless for a loss of $2,000 (point A)

• 115, the futures call will be at the money, but produces no gain or loss (point B)

• 120, the futures call will be in the money and will be exercised. You would buy the futures contract at the exercise price of 115 and then sell it for 120, thereby earning a 5-point gain ($5,000 profit) on the $100,000 Canada bond contract. Because you paid a $2,000 premium, however, the net profit is $3,000 (point C)


Figure 13-1. The Difference between Interest Rate Futures and Interest Rate Futures Options • the futures contract has a linear profit function --- there is a one-to-

one relationship between profits and the price of the underlying financial instrument

• the kinked profit curve for the option contract is nonlinear, meaning that profits don't always grow by the same amount for a given change in the price of the underlying financial instrument

• the reason for this nonlinearity is that the call option protects you from having losses that are greater than the amount of the $2,000 premium

• once the price of the underlying financial instrument rises above X, however, your profits on the call option grow linearly. They are, however, always less than the profits on the futures contract by exactly the $2,000 premium paid.


Currency FuturesHedging FX Risk

Example: Customer due € 20 million in two months, current € = $0.50

1. Forward agreeing to sell € 20 million for $10 million, two months in future

2. Sell € 20 million of futures


Currency Swaps

In a currency swap two parties effectively trade assets and liabilities denominated in different currencies.

The simplest currency swap is an agreement to sell a currency now at a given price and then repurchase it at a stated price on a specified future date. The difference between the two prices is called the swap rate.

Example:

A German bank might swap € for $ with a Canadian bank by agreeing to sell € 1 million at a price of € /$ = € 0.60 and to repurchase € 1 million a year later at a price of € /$ = € 0.70.

This currency swap allows the German bank to borrow $ and the Canadian bank to borrow €.


(Continued)

Often currency swaps are tied to debt issues. In particular, two parties issue debt denominated in different currencies and then agree to swap the proceeds of the debt issue and to repay each other's debts -- effectively transforming each debt into the other currency.

Example:

A Canadian company wants to borrow € 10 million. The company, however, believes that it can get better terms if it issues $-denominated bonds in Canada where it is well known, and then swap the $ for € with a German company that wants to borrow $ but for the same reasons finds it easier to borrow € in Europe --- see next slide.


Currency Swap Contract

CanadianCompany Can$ Coupon + Principal

CanadianInvestors

Can$Swap

Payments

DMSwap

Payments

GermanCompany DM Coupon + Principal

GermanInvestots


Using Currency Swaps to Manage Exchange Rate Risk

First Bank

Assets Liabilities

$-Denominated $188 m $-Denominated $50 m

€-Denominated $12 m €-Denominated $30 m

(€7.5 m @ $1.6/€) (€18.75 m @ $1.6/€)

Net worth $120 m


(Continued)

Considering the hypothetical balance sheet shown in the previous slide, if the $ depreciates relative to the €, € -denominated assets and liabilities will be worth more $.

Because the bank has more € -denominated liabilities than € -denominated assets, it will suffer losses.

For example, if the $/€ exchange rate increases to $1.7, then the bank will have a capital loss of $1.05 m, as can be seen in the following slide:


(Continued)

First Bank

Assets Liabilities

$-Denominated $188 m $-Denominated $50 m

€-Denominated 12.75 m €-Denominated $31.8 m

(€7.5 m @ $1.7/€) (€18.75 m @ $1.7/€)

Net worth $118.95

Total $200.75 Total $200.75


(Continued)

To reduce its exposure to the $/€ exchange rate risk,

the bank could swap $18 million of its € -denominated liabilities for $-denominated liabilities.

This would leave the bank with $12 million in € -denominated liabilities, which matches its $12 million of € -denominated assets.

With € -denominated assets = € -denominated liabilities, a change in $/€ exchange rate does not change the bank’s net worth.


Interest Rate Swaps

In an interest-rate swap, two unrelated parties take out loans. Then they agree to make each other’s periodic interest payments.

The two parties do not exchange their debts or lend each other money, but simply agree to make each other’s periodic interest payments as if they had swapped debts.

This kind of swap is illustrated by the hypothetical example in the next slide.


Interest-Rate Swap Contract


Hedging with Interest Rate Swaps

Reduce interest-rate risk for both parties1. Midwest converts $1m of fixed rate assets to rate-sensitive

assets, RSA , lowers GAP2. Friendly Finance RSA , lowers GAP

Advantages of swaps1. Reduce risk, no change in balance-sheet2. Longer term than futures or options

Disadvantages of swaps1. Lack of liquidity2. Subject to default risk

Financial intermediaries help reduce disadvantages of swaps


Cross-Currency Floating-to-Fixed Interest Rate Swaps

A cross-currency floating-to-fixed interest rate swap involves a fixed-rate loan denominated in one currency and a variable-rate loan denominated in another currency.

Example:

A small firm might borrow $ from a local bank at a floating-rate and then use a cross-currency interest-rate swap to swap payments with a large firm that has issued fixed-rate bonds denominated in €.


Cross-Currency Floating-to- Floating Swaps

In a cross-currency floating-to-floating swap, a floating-rate debt denominated in one currency is swapped for a floating-rate debt denominated in another currency.

Example:

A multinational firm with a loan in euros based on a short-term European interest rate can use a cross-currency floating-to-floating swap to transform its € loan into a dollar loan on the prime rate.

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Chapter 13 Financial Derivatives © 2005 Pearson Education Canada Inc