CALL & PUT OPTIONS

7/29/2019 CALL & PUT OPTIONS

1/76

1

Principles ofOptions and Option Pricing


2/76

2

We sent the first draft of our paper to the Journal of PoliticalEconomy and promptly got back a rejection letter. We thensent it to the Review of Economics and Statistics, where it

was also rejected.

Merton Miller and Eugene Famathen took an interest in thepaper and gave us extensive comments on it. They

suggested to the JPE that perhaps the paper was worthmore serious consideration. The journal then accepted the

paper.

- MILAN PATEL


3/76

3

OutlineIntroduction

Option principles

Option pricing


4/76

4

IntroductionInnovations in stock options have been

among the most important developments in

finance in the last 20 yearsThe cornerstone of option pricing is the

Black-Scholes Option Pricing Model

(OPM) Delta is the most important OPM progeny to

the portfolio manager


5/76

5

Option PrinciplesWhy options are a good idea

What options are

Standardized option characteristics

Where options come from

Where and how options trade

The option premium

Sources of profits and losses with options


6/76

6

Why Options Are A Good IdeaOptions:

Give the marketplace opportunities to adjust

risk or alter income streams that wouldotherwise not be available

Provide financial leverage

Can be used to generate additional income frominvestment portfolios


7/76

7

Why Options Are

A Good Idea (contd)The investment process is dynamic:

The portfolio managers needs to constantly

reassess and adjust portfolios with the arrival ofnew information

Options are more convenient and lessexpensive than wholesale purchases or sales

of stock


8/76

8

What Options AreCall options

Put options


9/76

9

Call OptionsA call option gives you the right to buy

within a specified time period at a specified

price

The owner of the option pays a cash

premiumto the option seller in exchangefor the right to buy


10/76

10

Practical Example

of A Call Option


11/76

11

Put OptionsA put option gives you the right to sell

within a specified time period at a specified

price

It is not necessary to own the asset before

acquiring the right to sell it


12/76

12

Standardized

Option CharacteristicsAll exchange-traded options have

standardized expiration dates

The Saturday following the third Friday ofdesignated months for most options

Investors typically view the third Friday of themonth as the expiration date


13/76

13

Standardized

Option Characteristics (contd)The striking priceof an option is the

predetermined transaction price

In multiples of $2.50 (for stocks priced $25.00or below) or $5.00 (for stocks priced higher

than $25.00)

There is usually at least one striking price

above and one below the current stock price


14/76

14

Standardized

Option Characteristics (contd)Puts and calls are based on 100 shares of the

underlying security

The underlying security is the security that theoption gives you the right to buy or sell

It is not possible to buy or sell odd lots ofoptions


15/76

15

Where Options Come FromIntroduction

Opening and closing transactions

Role of the Options Clearing Corporation


16/76

16

IntroductionIf you buy an option, someone has to sell it

to you

No set number of put or call options exists

The number of options in existence changes

every day Option can be created and destroyed


17/76

17

Opening and

Closing TransactionsThe first trade someone makes in a

particular option is an opening transaction

An opening transaction that is the sale of anoption is called writing an option


18/76

18

Opening and

Closing Transactions (contd)The trade that terminates a position by

closing it out is a closing transaction

Options have fungibilityMarket participants can reverse their positions by

making offsetting trades

E.g., the writer of an option can close out theposition by buying a similar one


19/76

19

Opening and

Closing Transactions (contd)The owner of an option will ultimately:

Sell it to someone else

Let it expire or

Exercise it


20/76

20

Role of the

Options Clearing CorporationThe Options Clearing Corporation (OCC):

Positions itself between every buyer and seller

Acts as a guarantor of all option trades Regulates the trading activity of members of

the various options exchanges

Sets minimum capital requirements Provides for the efficient transfer of funds

among members as gains or losses occur


21/76

21

OCC-Related

Information on the Web


22/76

22

Where and How Options TradeOptions trade on four principal exchanges:

Chicago Board Options Exchange (CBOE)

American Stock Exchange (AMEX)

Philadelphia Stock Exchange

Pacific Stock Exchange


23/76

23

Where and How

Options Trade (contd)AMEX and Philadelphia Stock Exchange

options trade via the specialist system

All orders to buy or sell a particular securitypass through a single individual (the specialist)

The specialist:Keeps an order book with standing orders from

investors and maintains the market in a fair andorderly fashion

Executes trades close to the current market price ifno buyer or seller is available


24/76

24

Where and How

Options Trade (contd)CBOE and Pacific Stock Exchange options

trade via the marketmaker system

Competing marketmakers trade in a specificlocation on the exchange floor near the orderbook official

Marketmakers compete against one another for

the publics business


25/76

25

Where and How

Options Trade (contd)Any given option has two prices at any

given time:

The bid priceis the highest price anyone iswilling to pay for a particular option

The asked priceis the lowest price at whichanyone is willing to sell a particular option


26/76

26

The Option PremiumIntrinsic value and time value

The financial page listing


27/76

27

Intrinsic Value and Time ValueThe price of an option has two components:

Intrinsic value:

For a call option equals the stock price minus thestriking price

For a put option equals the striking price minus the

stock price

Time valueequals the option premium minusthe intrinsic value


28/76

28

Intrinsic Value and

Time Value (contd)An option with no intrinsic value is out of

the money

An option with intrinsic value is in themoney

If an options striking price equals the stockprice, the option is at the money


29/76

29

The Financial Page ListingThe following slide shows an example from

the online edition of the Wall StreetJournal:

The current price for a share of Disney stock is$21.95

Striking prices from $20 to $25 are available

The expiration month is in the second column The option premiums are provided in the Last

column


30/76

30

The Financial Page Listing


31/76

31

The Financial

Page Listing (contd)Investors identify an option by company,

expiration, striking price, and type of

option:

Disney JUN 22.50 Call

CompanyExpiration Striking

Price

Type


32/76

32

The Financial

Page Listing (contd) The Disney JUN 22.50 Call is out of the money

The striking price is greater than the stock price

The time value is $0.25

The Disney JUN 22.50 Put is in the money

The striking price is greater than the stock price

The intrinsic value is $22.50 - $21.95 = $0.55 The time value is $1.05 - $0.55 = $0.50


33/76

33

The Financial

Page Listing (contd)As an option moves closer to expiration, its

time value decreases

Time value decay

An option is a wasting asset

Everything else being equal, the value of anoption declines over time


34/76

34

Sources of Profits and

Losses With OptionsOption exercise

Exercise procedures


35/76

35

Option ExerciseAn American option can be exercised at

any time prior to option expiration

It is typically not advantageous to exerciseprior to expiration since this amount to

foregoing time value

European optionscan be exercised only atexpiration


36/76

36

Exercise ProceduresThe owner of an option who decides to

exercisethe option:

Calls her broker Must put up the full contract amount for the

option

The premium is not a downpayment on the option

terms


37/76

37

Exercise Procedures (contd)The option writer:

Must be prepared to sell the necessary shares to

the call option owner

Must be prepared to buy shares of stock from

the put option owner


38/76

38

Exercise Procedures (contd)In general, you should not buy an option

with the intent of exercising it:

Requires two commissions

Selling the option captures the full value

contained in an option


39/76

39

Profit and Loss DiagramsFor the Disney JUN 22.50 Call buyer:

-$0.25

$22.50

$0

Maximum loss

Breakeven Point = $22.75

Maximum profit

is unlimited


40/76

40

Profit and Loss DiagramsFor the Disney JUN 22.50 Call writer:

$0.25

$22.50

$0

Maximum profit Breakeven Point = $22.75

Maximum loss

is unlimited


41/76

41

Profit and Loss DiagramsFor the Disney JUN 22.50 Put buyer:

-$1.05

$22.50

$0

Maximum loss

Breakeven Point = $21.45

Maximum profit = $21.45


42/76

42

Profit and Loss DiagramsFor the Disney JUN 22.50 Put writer:

$1.05

$22.50

$0

Maximum profitBreakeven Point = $21.45

Maximum loss = $21.45


43/76

43

Option Pricing Determinants of the option premium

Black-Scholes Option Pricing Model

Development and Assumptions of the model Insights into the Black-Scholes Model

Delta

Theory of put/call parity Stock index options


44/76

44

Determinants of the

Option PremiumMarket factors

Accounting factors


45/76

45

Market FactorsStriking price

For a call option, the lower the striking price,

the higher the option premium

Time to expiration

For both calls and puts, the longer the time toexpiration, the higher the option premium


46/76

46

Market Factors (contd)Current stock price

The higher the stock price, the higher the call

option premium and the lower the put optionpremium

Volatility of the underlying stock The great the volatility, the higher the call and

put option premium


47/76

47

Market Factors (contd)Dividend yield on the underlying stock

Companies with high dividend yields have a

smaller call option premium than companieswith low dividend yields

Risk-free interest rate The higher the risk-free rate, the higher the call

option premium


48/76

48

Accounting Factors

Stock splits:

The OCC will make the following adjustments:The striking price is reduced by the split ratio

The number of options is increased by the split ratio

For odd-lot generating splits:

The striking price is reduced by the split ratioThe number of shares covered by your options is

increased by the split ratio


49/76

49

Black-Scholes

Option Pricing Model

The Black-Scholes OPM:

1 2

2

1

2 1

( ) ( )

ln( / ) ( / 2)

rtC S N d Ke N d

S K R t d

t

d d t


50/76

50

Black-Scholes

Option Pricing Model (contd)

Variable definitions:

C= theoretical call premium

S= current stock price t= time in years until option expiration

K= option striking price

R = risk-free interest rate


51/76

51

Black-Scholes


Variable definitions (contd):

= standard deviation of stock returns

N(x)= probability that a value less than x willoccur in a standard normal distribution

ln = natural logarithm

e = base of natural logarithm (2.7183)


52/76

52

Black-Scholes


Example

Stock ABC currently trades for $30. A call option on ABCstock has a striking price of $25 and expires in three

months. The current risk-free rate is 5%, and ABC stock

has a standard deviation of 0.45.

According to the Black-Scholes OPM, but should be the

call option premium for this option?


53/76

53

Black-Scholes


Example (contd)

Solution: We must first determine d1 and d2:2

1

2

ln( / ) ( / 2)

ln(30 / 25) 0.05 (0.45 / 2) 0.25

0.45 0.25

0.1823 0.03780.978

0.225

S K R t d

t


54/76

54

Black-Scholes


Example (contd)

Solution (contd):

2 1

0.978 (0.45) 0.25

0.978 0.225

0.753

d d t


55/76

55

Black-Scholes


Example (contd)

Solution (contd): The next step is to find the normalprobability values for d1 and d2. Using ExcelsNORMSDIST function yields:

1

2

( ) 0.836

( ) 0.774

N d

N d


56/76

56

Black-Scholes


Example (contd)

Solution (contd): The final step is to calculate the optionpremium:

1 2

(0.05)(0.25)

( ) ( )

$30 0.836 $25 0.774$25.08 $19.11

$5.97

rtC S N d Ke N d

e


57/76

57

Using Excels

NORMSDIST Function

The Excel portion below shows the input

and the result of the function:


58/76

58

Development and

Assumptions of the Model

Introduction

The stock pays no dividends during the options

life

European exercise terms

Markets are efficient

No commissions

Constant interest rates

Lognormal returns


59/76

59

Introduction

Many of the steps used in building theBlack-Scholes OPM come from:

Physics

Mathematical shortcuts

Arbitrage arguments

The actual development of the OPM iscomplicated


60/76

60

The Stock Pays no Dividends

During the Options Life

The OPM assumes that the underlying

security pays no dividends

Valuing securities with different dividend

yields using the OPM will result in the same

price


61/76

61

The Stock Pays no Dividends

During the Options Life

The OPM can be adjusted for dividends:

Discount the future dividend assumingcontinuous compounding

Subtract the present value of the dividend fromthe stock price in the OPM

Compute the premium using the OPM with theadjusted stock price


62/76

62

European Exercise Terms

The OPM assumes that the option is

European

Not a major consideration since very few

calls are ever exercised prior to expiration


63/76

63

Markets Are Efficient

The OPM assumes markets are

informationally efficient

People cannot predict the direction of themarket or of an individual stock


64/76

64

No Commissions

The OPM assumes market participants do

not have to pay any commissions to buy or

sellCommissions paid by individual can

significantly affect the true cost of an option

Trading fee differentials cause slightly differenteffective option prices for different market

participants


65/76

65

Constant Interest Rates

The OPM assumes that the interest rateR inthe model is known and constant

It is common use to use the discount rate ona U.S. Treasury bill that has a maturityapproximately equal to the remaining life of

the option This interest rate can change


66/76

66

Lognormal Returns

The OPM assumes that the logarithms of

returns of the underlying security are

normally distributed

A reasonable assumption for most assets on

which options are available

I i ht I t th


67/76

67

Insights Into the

Black-Scholes Model

Divide the OPM into two parts:

1 2( ) ( )rt

C S N d Ke N d

Part A Part B

I i ht I t th


68/76

68

Insights Into the

Black-Scholes Model (contd)

Part A is the expected benefit from

acquiring the stock:

Sis the current stock price and the discountedvalue of the expected stock price at any future

point

N(d1) is a pseudo-probability

It is the probability of the option being in the money

at expiration, adjusted for the depth the option is in

the money

I i ht I t th


69/76

69

Insights Into the


Part B is the present value of the exercise

price on the expiration day:

N(d2) is the actual probability the option will bein the money on expiration day

I i ht I t th


70/76

70

Insights Into the


The value of a call option is the difference

between the expected benefit from

acquiring the stock and paying the exerciseprice on expiration day


71/76

71

Delta

Delta is the change in option premiumexpected from a small change in the stock

price, all other things being equal:

where the first partial derivative of the call premium

with respect to the stock price

C

S

C

S


72/76

72

Delta (contd)

Delta allows us to determine how many

options are needed to mimic the returns of

the underlying stock

Delta is exactly equal toN(d1)

E.g., ifN(d1) is 0.836, a $1 change in the priceof the underlying stock price leads to a change

in the option premium of 84 cents


73/76

73

Theory of Put/Call Parity

The following variables form an interrelatedsecurities complex:

Price of a put

Price of a call

The value of the underlying stock

The riskless rate of interest

If put/call parity does not hold, arbitrage ispossible

Th f


74/76

74

Theory of

Put/Call Parity (contd)

The put/call parity relationship:

(1 )where price of a call

price of a put

option striking pricerisk-free interest rate

time until expiration in years

T

KC P S

R

C

P

K

R

T


75/76

75

Stock Index Options

A stock index option is the option

exchanges most successful innovation

E.g., the S&P 100 index option

Index options have no delivery mechanism

All settlements are in cash


76/76

76

Stock Index Options (contd)

The owner of an in-the-money index call

receives the difference between the closing

index level and the striking price

The owner of an in-the-money index put

receives the difference between the strikingprice and the index level

Documents

CALL & PUT OPTIONS