Citibank options

COURSE OBJECTIVESWhen you complete this workbook, you will be able to: n Understand basic option transactions and terminology n Identify the benefits of options from the perspective of

November 1999

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Course Overview viiCourse Objectives viiThe Workbook viii

Unit 1: Fundamentals of Options

Introduction 1-1Unit Objectives 1-1The Language of Options 1-1

Contract Terminology 1-2Option Price Terminology 1-3Basic Option Transactions 1-5

Payoff Diagram 1-5Buying a Call 1-6Selling a Call 1-8Buying a Put 1-8Selling a Put 1-9Options Markets 1-11

Exchange Market 1-12Over-the-Counter (OTC) Market 1-13Summary 1-13Progress Check 1 1-15

Unit 2: Option Applications

Introduction 2-1Unit Objectives 2-1Option Payoffs 2-1Option Applications 2-2

Hedging 2-3Yield Enhancement 2-3

Unit 2: Option Applications (Continued)

Trading Profits 2-4Arbitrage 2-4Option-Related Instruments 2-5

Warrants 2-6Rights 2-7Callable Bonds 2-7Puttable Bonds 2-7Convertible Bonds 2-8Swap Options 2-8Summary 2-8Progress Check 2 2-11

Unit 3: Option Combinations

Introduction 3-1Unit Objectives 3-1Option Payoffs 3-1Spread Trades 3-11

Bull Spread 3-11Bear Spread 3-12Summary 3-13Progress Check 3 3-15

Unit 4: Option Valuation

Introduction 4-1Unit Objectives 4-1Variables in Option Valuation 4-2Effect of Interest-Rate Movement and Time 4-3

Unit 4: Option Valuation (Continued)

Call Price Calculation 4-7Basis for Assumptions 4-9Volatility 4-11

Determining Volatility 4-12Summary 4-13Progress Check 4.1 4-15Sensitivity to Price Factors 4-19

Strike Level Versus Forward Rate 4-19Volatility 4-20Market Price – Spot / Forward 4-21Time to Maturity 4-21Interest Rates 4-21Summary 4-23Progress Check 4.2 4-25

Unit 5: Customer Option Strategies

Introduction 5-1Unit Objectives 5-1Interest-Rate Caps and Floors 5-2

Caps 5-2

Pricing a Cap 5-3Floors 5-5

Pricing Floors 5-5All-In-Cost of Borrowing 5-6

Collar 5-9Zero-Cost Collar 5-11Ratio Spread 5-12Summary 5-13Progress Check 5 5-15

Unit 6: Currency, Equity, and Commodity Options

Introduction 6-1Unit Objectives 6-1Foreign Currency Options 6-1

Uses of Currency Options 6-3Pricing of Foreign Currency Options 6-4Equity Options 6-5

Uses of Equity Options 6-6Pricing of Equity Options 6-7Commodity Options 6-7

Uses of Commodity Options 6-8Pricing of Commodity Options 6-9Summary 6-10Progress Check 6 6-13

Unit 7: Option-Related Risk

Introduction 7-1Unit Objectives 7-1Managing Option Book Price Risk 7-2

Price of the Underlying Asset 7-3Time-to-Maturity Risk 7-4Volatility Risk 7-5Interest-Rate Risk 7-6Credit Risk 7-6Summary 7-7Progress Check 7 7-9

Index

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Introduction

COURSE OVERVIEW

The purpose of this workbook is to introduce options as they apply across a whole range ofmarket factors We will use a “building block” approach, beginning by defining some of thejargon as it applies to just one market factor: interest rates We then will build to an

intermediate level of understanding and analyze options by using bonds and LIBOR rates asour benchmarks Finally, we will show that the general concepts apply across an entire range

of markets, including foreign exchange, equities, and commodities

Options, in various forms, have been around for centuries The market in options received amajor boost in the early 1970s as a formal option pricing methodology came into

widespread use Options on stocks were first traded on an organized exchange in 1973;since then, the volume of option and option-linked transactions has grown dramatically.Options are now traded on exchanges throughout the world In addition, huge volumes in alltypes of underlying assets are being traded in the over-the-counter market A growing

understanding and acceptance among potential users suggests that growth will be sustainedfor the foreseeable future

Each unit covers an aspect of option transactions The units are:

UNIT 1 - Fundamentals of Options

UNIT 2 - Option Applications

UNIT 3 - Option Combinations

UNIT 4 - Option Valuation

UNIT 5 - Customer Option Strategies

UNIT 6 - Currency, Equity, and Commodity Options

UNIT 7 - Option-Related Risks

COURSE OBJECTIVES

When you complete this workbook, you will be able to:

n Understand basic option transactions and terminology

n Identify the benefits of options from the perspective of option users

n Analyze the combination of an underlying position with options or a

combination of options

n Understand basic option pricing methodology

n Recognize the sensitivity of option prices to changing market factors

n Recognize how option positions are managed from the bank’s perspective

THE WORKBOOK

This workbook is designed to give you complete control over your own learning The

material is divided into workable sections, each containing everything you need to masterthe content You can move through the workbook at your own pace and go back to reviewideas that you didn’t completely understand the first time Each unit contains:

lesson that you are expected to learn

section explains the content in detail

appear in bold face the first time they

appear in the text

þ Progress Checks – which do exactly what they say — checkyour progress Appropriate questions are

presented at the end of each unit, or withinthe unit in some cases You will not begraded on these by anyone else; they are

to help you evaluate your progress Each set

of questions is followed by an Answer Key

If you have an incorrect answer, weencourage you to review the correspondingtext and find out why you made an error

In addition to these unit elements, the workbook includes:

Exotic Options

Financial Derivatives Exchanges

Spansih) of definitions of all key termsused in the workbook

in the workbook

Since this is a self-instructional course, your progress will not be supervised We expectyou to complete the course to the best of your ability and at your own speed Now that youknow what to expect, please begin with Unit 1 Good luck!

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Unit 1

The options market is a growing business with its own unique language In this unit, youwill be introduced to basic option terminology, contract terms and conditions, and optionmarkets These concepts will provide you with a foundation for understanding optiontransactions

UNIT OBJECTIVES

When you complete this unit, you will be able to:

n Identify the terms and conditions required for an option contract

n Define common terminology used with options

n Recognize the relationships of items in a payoff diagram

n Calculate an option party’s profit or loss

n Differentiate between exchange-traded options and over-the-counter

THE LANGUAGE OF OPTIONS

We begin our study of options by defining an option contract andpresenting basic option contract and pricing terminology

The writer is short of an option position while the holder is long of

an option position A short position results from the sale of a put or

a call A long position results from the purchase of a put or a call.

With this definition in mind, let’s look at some basic terms thatapply to an option contract and option pricing

n A description of the underlying asset, which may be

physically settled or cash settled at maturity

n Whether the option is a call or a put

n The exercise price

n The maturity or time to expiration of the option

n Whether the option is American-style or European-style

Here is a brief definition of each of these requirements

U NDERLYING ASSET

The underlying asset is the asset or non-physical

“something” that the option holder has the right tobuy or sell The underlying asset may be interestrates, debt instruments, foreign currencies, stocks,

C ALL A call is the right to buy a specified quantity

of an underlying

P UT A put is the right to sell a specified quantity

of an underlying

E XERCISE ( STRIKE ) PRICE

The price at which an option holder can exercisethe right to buy or sell the underlying is known as

the exercise price or the strike price.

A MERICAN OPTION

The holder of an American option has the right

to exercise the option at any time overthe life of the option, up to and including the

expiration date.

E UROPEAN OPTION

The holder of a European option has the right to

exercise the option only at the time of theoption’s maturity

Option Price Terminology

whether the option is in-, at- or out-of-the-money These terms

refer to the relationship between the price or rate on the underlyingand the option’s exercise price These are important concepts that

we will refer to often, so review them carefully!

P REMIUM The premium is the price of the option, which is

paid up front by the option holder to the optionwriter for the right stated in the option

I N - THE - MONEY (ITM)

An in-the-money (ITM) option has an exercise

price that is more advantageous than the currentmarket price of the underlying For example, a call

on a bond is ITM if the bond price is above theexercise price of the option The more the option isITM, the more expensive it is

O UT - OF THE - MONEY (OTM)

-In an out-of-the-money (OTM) option, the price

on the underlying is above the exercise price in thecase of a put, or below it in the case of a call Themore the option is OTM, the cheaper it is

A T - THE - MONEY (ATM)

The term at-the-money (ATM) can be confusing,

because it can be relative to either the spot price(price for immediate delivery) or the forward price

At-the-money spot (ATMS) is the term for an

option with an exercise price that is set the same as

the prevailing market price of the underlying An

at-the-money forward (ATMF) option is one with an

exercise price set at the same level as the prevailingforward price of the underlying An at-the-moneyspot (ATMS) option will be cheaper than an ITMoption but more expensive than an OTM option

I NTRINSIC VALUE

Intrinsic value refers to the amount by which

an option is in-the-money For example, theintrinsic value of an ITM call on a bond is theamount by which the bond price exceeds theexercise price The intrinsic value of an ITMput is the amount by which the exercise priceexceeds the stock price If the calls or puts areeither ATM or OTM, their intrinsic values are zero

An option’s intrinsic value can never be negative

because there is no obligation to exercise theoption

BASIC OPTION TRANSACTIONS

Now that you know the basic terminology of options, you are ready

to learn about option transactions There are four basic transactions

to which a party to an option can agree:

n Buy a call (acquire the right to buy an underlying asset)

n Sell a call (sell the right to buy an underlying asset)

n Buy a put (acquire the right to sell an underlying asset)

n Sell a put (sell the right to sell an underlying asset)

Payoff Diagram

Profit / loss

profile

To help you understand how the four transaction types work, we will

illustrate them with payoff diagrams A payoff diagram is a graph

that depicts the profit and loss profile for one party to an optioncontract over a range of prices or rates on the underlying

In Figures 1.1 through 1.5, assume that the underlying asset is abond, and that the bond’s price will vary with changes in marketinterest rates, specifically a change in the interest rate over the tenor

of the bond

We will use the following notation in our analysis:

P / L = Profit or loss (vertical axis)

B = Bond price (horizontal axis)

X = Exercise price

P m = Premium

Value at

expiration

To illustrate the four transaction types, we will consider the value

at expiration of a European-style option on the bond Recall that in

a European option, the option holder has the right to exercise theoption only at the time of the option’s maturity

from it If, at expiration, the bond price is less than the exercise

price, the option is worthless (because it is possible to buy the bond

in the market for less than the exercise price) Therefore, the optionwill not be exercised

If the bond price is greater than the exercise price at expiration, the

value of the option is equal to the difference between the bond priceand the exercise price (intrinsic value) The call holder will exercisethe option, buying the bond for price X and selling it in the marketfor price B, generating a profit of B-X

This long call position (position of the holder who has purchased

a call option) is illustrated in Figure 1.1

Figure 1.1: A long call position at maturity, without premium

Upon exercise (X), the call holder becomes the owner of the bond;the payoff line turns upward at a 45o angle, indicating a one-to-one relationship between the bond price and the option value atexpiration Notice that the payoff line takes on the shape of a

“hockey stick.”

P / L

+

B X

–

shifts the payoff profile down for the holder

Figure 1.2: A long call position at maturity, with premium

Break-even

point

Notice that, in this case, the payoff line crosses the horizontal (bond price) line at X + Pm (exercise price plus call premium) This

is the call holder’s break-even point Note that the holder will

exercise the option whenever the bond price is greater than the exercise price — even when the price is less than the break-even — because the loss will be less than if the option is not exercised

Selling a Call

In the previous section, we discussed the payoff primarily from the call option holder’s view Now, let’s consider how the payoff diagram looks from the call option writer’s view If we compare Figure 1.2 with Figure 1.3, we see that the payoff for selling a call

is the opposite of buying a call The writer collects the premium,

Pm If the price of the bond moves beyond the exercise price, the call holder will exercise the option; so the writer’s payoff line turns downward at a 45o angle and crosses the bond price line at X + Pm

(exercise plus call premium) The crossing point is the call writer’s break-even point If the bond price moves beyond this point, the writer incurs a loss This short call position (position of the writer who has sold the call) is shown in Figure 1.3

Figure 1.3: A short call position at maturity

Figure 1.4: A long put position at maturity

Selling a Put

What will the payoff diagram look like if the writer sells the right tosell the bond? If we compare Figure 1.4 with Figure 1.5, we see thatthe payoff for selling a put is the reverse of buying a put The payoffline crosses the bond price axis at X - Pm (exercise price minus theput premium) and continues upward until it breaks into a horizontalline at the exercise price (X) Here, we see that the put writer profits

if the bond’s value goes above the break-even point

Figure 1.5: A short put position at maturity

An example will help clarify the positions of the option holderand writer

Compare the payoff diagrams for the two parties (in Figure 1.6) andthen read on to see how the positions of the option parties areaffected by changes in the price of the underlying.

Figure 1.6: Payoff profiles for both parties at maturity

Let’s consider three possible price changes to see how they affectthe positions of the option parties at contract expiry

Scenario 1 In six months, the bond is trading at $105.00 The call holder exercises

the option at $100.00 For a total outlay of $102.00, the holder nowowns an asset worth $105.00

–

P / L

+

B 2.00{

102 100

–

Return to Call Holder Return to Call Writer

Scenario 3 In six months, the bond is trading at $101.00 The call holder

exercises the option because the bond’s price ($101.00) is higherthan the exercise price ($100.00) The call holder now owns an assetworth $101.00 Note that the option holder does not make a profit

on the option investment because, at expiration date, the bond’smarket price ($101.00) does not cover the cost of the bond boughtunder the option plus the premium ($102.00) However, the loss isless than it would have been had the option gone unexercised at thislevel

As you can see, the trading price at expiration determines whetherthe call holder will exercise the option and which party, if either,profits or loses

Bank’s role In this example, we assumed that the two parties engaged in the

option contract had different views and, therefore, different

objectives A bank that establishes itself as a market maker in

options (a counterparty to any option holder or writer) takes onpositions that do not necessarily correspond to its own views In thiscase, the bank will offset the risk by laying off that position in themarket The bank does an equal and opposite transaction in the option

market (i.e., as a writer, it will buy back an equivalent option; as a

buyer; it will sell an equivalent option), or it will hedge in the cash

market (refer to Unit 7)

OPTIONS MARKETS

Option puts and calls are traded in two major option markets:

exchange and over-the-counter

Exchange Market

Exchange-traded option contracts are purchased and sold on anorganized exchange by exchange members In order to generatesufficient liquidity, they tend to be standardized and limited incomplexity Options were first traded on exchanges and theycontinue to transact large volumes of contracts around the world.The exchange where an option is traded may depend on the

Stock options Many exchanges trade stock options on individual stocks Those in

the US include the Chicago Board Options Exchange (CBOE), theNew York Stock Exchange (NYSE), and PHLX

Stock index

options

Stock index options provide an alternate way to take a position in

an equity market Unlike the other options we’ve discussed, which

settle with a physical delivery of the asset, index options settle on

a cash difference based on the index value at the end of the day

on which exercise takes place The two most popular stock indexoptions in the US are the S&P (Standard and Poor’s) 100 and S&P

500, which are both traded on the Chicago Board Options Exchange(CBOE)

Futures options In a futures option, the underlying asset is a futures contract, which

is a standardized agreement to buy or sell a specific quantity of anasset at a defined time in the future Usually, the futures contractmatures shortly after the expiration of the option So, when theholder of a call option exercises the option, the holder acquires fromthe writer a long position in the underlying futures contract, plus acash amount equal to the excess of the futures price over theexercise price Options on interest-rate futures — particularly the T-Bond and Eurodollar futures traded on the Chicago Board of Trade(CBOT) and the Chicago Mercantile Exchange (CME), respectively

We discuss the different types of options in greater detail in Unit 6.

Over-the-Counter (OTC) Market

Over-the-counter (OTC) contracts are created outside the

exchanges by dealers trading directly with counterparties over thetelephone, screen, or telex The OTC markets provide tailoredproducts to meet specific requirements

The choice of market depends on the level of tailoring, liquidity,and credit concerns Some exchanges are moving to bridge the gapbetween the exchange market and the OTC market by introducingoption products with more flexible terms and conditions

SUMMARY

A party to an option can:

n Buy a call (acquire the right to buy an underlying asset)

n Sell a call (sell the right to buy an underlying asset)

n Buy a put (acquire the right to sell an underlying asset)

n Sell a put (sell the right to sell an underlying asset)

We can use payoff diagrams to illustrate the value of a call or a putfrom the option writer’s or the option holder’s view

The two parties to an option contract take a short or long position,depending on their views of the future value of the underlying

A holder or writer may counteract the option risk by offsetting itwith an opposite transaction

Standardized options are traded on exchanges; options that aretailored to customers’ needs are traded in the more active over-the-counter market.

You have completed Unit 1, Fundamentals of Options Please complete the Progress

Check to test your understanding of the concepts and check your answers with the AnswerKey If you answer any questions incorrectly, please reread the corresponding text to

clarify your understanding Then, continue to Unit 2, Option Applications.

# PROGRESS CHECK 1

Directions: Determine the correct answer(s) to each question Check your answers with

the Answer Key on the next page

Question 1: Which three of the following terms and conditions are required for any

option contract?

_ a) Explicit definition of the underlying

_ b) The intrinsic value of the option

_ c) Price at which the underlying can be bought or sold

_ d) A guaranteed interest rate

_ e) The transaction market (exchange-traded or OTC)

_ f) Time period during which the holder may exercise the option

Question 2: Match the following terms to their definitions

Option a) Investor who acquires the right to buy a specific asset

at a specific price on or before a specific date Put b) Right to buy or sell a specific quantity of a specific

asset at a specific price on or before a specific date Call c) Right to sell a specific quantity of a specific asset at

a specific price on or before a specific date Call holder d) Investor who sells the right to buy a specific asset at

a specific price on or before a specific date Call writer e) Investor who acquires the right to sell a specific asset

at a specific price on or before a specific date Put holder f) Right to buy a specific asset at a specific price on or

before a specific date Put writer g) Investor who sells the right to sell a specific asset

at a specific price on or before a specific date

Question 2: Match the following terms to their definitions.

b Option a) Investor who acquires the right to buy a specific asset

at a specific price on or before a specific date

c Put b) Right to buy or sell a specific quantity of a specific

asset at a specific price on or before a specific date

f Call c) Right to sell a specific quantity of a specific asset at

a specific price on or before a specific date

a Call holder d) Investor who sells the right to buy a specific asset at a

specific price on or before a specific date

d Call writer e) Investor who acquires the right to sell a specific asset

at a specific price on or before a specific date

e Put holder f) Right to buy a specific asset at a specific price on or

before a specific date

g Put writer g) Investor who sells the right to sell a specific asset

at a specific price on or before a specific date

PROGRESS CHECK 1

(Continued)

Question 3: Match each term to its definition You may use the terms more than once:

a) At-the-money (spot)b) In-the-money (spot)c) Out-of-the-money (spot)

Put with an exercise price of 105 when the present market price for theunderlying asset is 108

Put with an exercise price of 110 when the present market price for theunderlying asset is 108

Call when the exercise price is the same as the present market price forthe underlying asset

Call with an exercise price of 107 when the present market price for theunderlying asset is 111

Call with an exercise price of 110 when the present market price for theunderlying asset is 108

Question 4: Which one of the following statements is true?

a) OTC options can be designed to expire on a date specified by the

option writer

b) Stock index options are physically settled with a portfolio of stocks

on the day in which exercise takes place

c) Currency options are principally traded on the CBOE

d) An option on a futures contract typically matures shortly before the

underlying futures contract

ANSWER KEY

Question 3: Match each term to its definition You may use the terms more than once:

a) At-the-money (spot)b) In-the-money (spot)c) Out-of-the-money (spot)

c Put with an exercise price of 105 when the present market price for the

underlying asset is 108

b Put with an exercise price of 110 when the present market price for the

underlying asset is 108

a Call when the exercise price is the same as the present market price for

the underlying asset

b Call with an exercise price of 107 when the present market price for the

underlying asset is 111

c Call with an exercise price of 110 when the present market price for the

underlying asset is 108

Question 4: Which one of the following statements is true?

d) An option on a futures contract typically matures shortly before the underlying futures contract.

of 60 cents for an exercise price of 92.75 (Note: You will recall from theFutures workbook that the Eurodollar futures price is the interest rateindexed off 100 and represents a 3-month forward interest rate for the periodMarch – June of 7.25%; i.e., 100 - 92.75 = 7.25%.)

Position of call holder

+

Eurodollar Future

93.35

92.75

–

Position of call writer

+

Eurodollar Future

93.35 92.75

–

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Question 7: If the market is at 94.75 on the exercise date and the call holder exercises the

option, what is the call holder’s profit?

a) $0.90

b) $1.40

c) $1.50

d) $2.00

Question 8: What is the call writer’s profit if the market is at 91.50 on exercise date and

the call holder does not exercise the option?

a) $0.50

b) $0.60

c) $1.25

d) $1.75

Though the call holder does not make a profit until the market price

of the futures contract is greater than $93.35 (the cost of the contract bought under the option plus the premium), the call holder is likely to exercise the option because the loss is less than it would be if s/he does not exercise the option.

Question 7: If the market is at 94.75 on the exercise date and the call holder exercises the

option, what is the call holder’s profit?

b) $1.40

$94.75 - 93.35 = $1.40

Question 8: What is the call writer’s profit if the market is at 91.50 on exercise date and

the call holder does not exercise the option?

b) $0.60

The call writer’s profit is the premium, $.60.