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This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

Intro to Options

BUY LOW SELL HIGH “Derivatives Are Financial Weapons Of Mass Destruction”

Warren Buffet

Draft version

Organized trading of standardized option contracts began in 1973 (prior to that had

existed OTC)...immediately the CBOE was a big hit...OTC options still exist and are

doing very well...more customizable, higher transaction costs but most options are now

traded on organized exchanges (CBOE).

What are derivatives? • Derivative security

– a financial security whose payoff is linked to another previously issued

security

• An agreement between two parties to exchange a standard quantity of an asset at a

predetermined price at a specified date in the future

What are options? A financial option is a contract that gives the holder, the RIGHT BUT NOT THE

OBLIGATION TO BUY OR SELL an underlying asset at a pre-specified time.

• There are two types of options: Call Options and Put Options. But before delving into the two different kinds of options,

let us look at the two parties involved + some basic terminologies:

The two parties involved:

Type of Option Holder Writer

Call Option Has the right but not the

obligation to BUY

Has the obligation to SELL

Price = Call Premium C

Put Option Has the right but not the

obligation to SELL

Has the obligation to BUY

Price = Put Premium P

In your lives you already know that nothing comes free right? In options too there is no

escape. Since you are afraid that the price will go up or down and need “insurance”, you

gotta pay for it! That is what is known as the Premium P for PUT options and C for

call options.

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

Hence you see the holders have a CHOICE but the writers’ position is pretty risky right?

As they are obligated to fulfill their part of the bargain!

Exercise Price or the Strike Price denoted X  Price that is pre-determined by the

contract. This is the price at which the holder buys (call) and the holder sell (put) and the

price at which the writers are obligated to sell or buy no matter what.

Note: If the price does not go in the direction of the call holder (up) or put holder (down)

they will not exercise the option and just pay the premium.

Expiration Date

– The last date on which an option holder has the right to exercise the option

Expectation of CALL HOLDER stock price is going to go up so they can buy at the

lower exercise price and sell at the prevailing price in the market. Here you are betting

that the underlying asset price rises. Call holders are said to be in a LONG position.- if

you "long a call" you purchased the call option and if the stock price is above the

strike price then you want to exercise the option. You are expecting the market

price of the underlying asset to rise above strike price by maturity.

Expectation of CALL WRITER stock price is not going to go up the holder will not

exercise and they will win the PREMIUM C.

Expectation of PUT HOLDER stock price is going to go down so they can sell at the

higher exercise price and buy at the prevailing price in the market. Here you are betting

that the underlying asset price falls.- if you "long a put option" you are betting the

market price will go down and bought the option to sell - if the stock price is below

the strike price then you exercise the option

Expectation of PUT WRITER stock price is not going to go down the holder will not

exercise and they will win the PREMIUM P.

Note: I know it might be confusing but remember the holder of a call (BUYS) while

the holder of a Put (SELLs)

Summary!

Call Option: an option that gives a purchaser the right, but not the obligation, to buy the

underlying security from the writer of the option at a prespecified exercise price on a

prespecified date .Call contract is for 100 shares

Put option an option that gives a purchaser the right, but not the obligation, to sell the

underlying security to the writer of the option at a prespecified price on a prespecified

date. Put contract is for 100 shares

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

 American option - can be exercised at any time before the expiration date

 European option - can only be exercised on the expiration date

 Note: The names American and European have nothing to do with the location

where the options are traded.

 At-the-money

o Describes an option whose exercise price is equal to the current stock

price

 In-the-money

o Describes an option whose value, if immediately exercised, would be

positive

 Out-of-the-money

o Describes an option whose value, if immediately exercised, would be

negative

 Deep in-the-money

o Describes an option that is in-the-money and for which the strike price and

the stock price are very far apart

 Deep out-of-the-money

o Describes an option that is out-of–the-money and for which the strike

price and the stock price are very far apart

 If the call is in-the-money, it is worth ST – E.

 If the call is out-of-the-money, it is worthless:

 C = Max[ST – E, 0]

 If the put is in-the-money, it is worth E – ST

 If the put is out-of-the-money, it is worthless

 P = Max[E – ST, 0]

-Naked position - an option position when the owner does not own the underlying asset.

-Covered position- an option position when the owner does own the underlying asset.

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

OPTION QUOTES: STRIKE

Strike

Price

Stock

Price

Expiration

OPTION QUOTES: OPTION PRICE

Option Price (cost

would be 100*0.25

= $25 plus

commission)

Change from

previous day

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

OPTION QUOTES: MONEYNESS

Out of the Money Call

192.30 – 195.00 = -2.70

Out of the Money Put

180.00 – 192.30 = -12.30

In the Money Put

192.50 – 192.30 = -0.20

OPTION QUOTES: VOLUME

Volume: Number

of contracts traded

Open Interest:

Number of contracts

outstanding

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

Payoffs from Options

Imagine you think that the price of ABC will go up in value. Of course you are not sure.

EG: Consider a NOV 2020 maturity call option on a share of ABC stock with an exercise

price X of $105 per share selling on AUG 4th 2020 for $5. The expiration date is NOV

20 th

Let us look at the graph/figure So if you are the holder you can buy at $105

on or before NOV 20th. While if you are the writer you are obligated to sell at

$105 before NOV 20th

PAYOFF Profit Profit Loss

Call holder St> X+C Unlimited Limited to C

Call Writer St<X Limited to C Unlimited

Put holder X> St-P Unlimited Limited to P

Put Writer St>X Limited to P Unlimited

Profit/ loss Call HOLDER

When do you exercise? What is your break even stock price?

When do you start making +ve profits? Negative profits?

Profit/loss

100 105 110 115 120 125 130 135 St

-5

Note: The figure is not drawn to scale!

General Rule for call holders Profit when St > C+X

Break even (profit/loss 0) @ C+X

When St< X do not exercise

Max Loss = Premium

Max Profit = Unlimited = St – C – X = Profit from the transaction

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

Case 1

Price of ABC rises to $112 on NOV 20 th ! (Holder has the right not

OBLIGATION , BUT Writers HAVE OBLIGATION) Profit of holder = ST-C-X = 112-5-105 =$2/share

Break even = C+X =105+5=110 So if stock price at expiration is $110 you neither

make a profit or a loss.

Case 2

Price of ABC falls to $90 at expiration! Holder does NOT exercise and MAX loss of premium =$5/share

Profit/ loss WRITER

Profit/loss

100 105 110 115 120 125 130 135 St

-5

Note: The figure is not drawn to scale!

General Rule for call writers  Profit when St <X

When St< X call holders do not exercise

Max Loss = UNLIMITED

Some important points to remember:

• The payoffs of the call holder & writer are MIRROR Images of each

other. My figures are not drawn to scale but still they do look like mirror

images. Similarly, the payoffs of the put holder & writer are MIRROR

Images of each other.

• Also when computing the profit and loss do not forget to take into

consideration the premium paid/received. • Which brings us to a very important point the concept of “Zero sum

game” – all derivatives are "zero-sum" games. That means your gains come

from the losses of others. For instance iff call holder makes a profit of +100,

the call writer will make a loss of -100 ceteris paribus and hence the resulting

sum will equal 0.

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

Now imagine that you think that the price ORANGE share is going to go down.

EG: Consider a NOV 2020 maturity put option on a share of ORANGE stock with an

exercise price X of $105 per share selling on AUG 4th 2020 for $5. The expiration date is

NOV 20th.

Let us look at the graph/figure So if you are the holder you can SELL at

$105 on or before NOV 20th. While if you are the writer you are obligated to

BUY at $105 before NOV 20th

PAYOFF Profit Profit Loss

Call holder St> X+C Unlimited Limited to C

Call Writer St<X Limited to C Unlimited

Put holder X> St-P Unlimited Limited to P

Put Writer St>X Limited to P Unlimited

Profit/ loss Put HOLDER

When do you exercise? What is your break even stock price?

When do you start making +ve profits? Negative profits?

Profit/loss

90 95 100 105 110 115 120 125 ST

-5

Note: The figure is not drawn to scale!

Break even is X-P (105-5)=$100

General Rule for call holders Profit when St < X-C

When St> X do not exercise

Max Loss = Premium

Max Profit = Unlimited = X-P-St = Profit from the transaction

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

Case 1

Price of ORANGE falls to $96 on NOV 20 th

Profit of holder = X-P-ST = 105(sell)-5(P)-96(St) =$4/share

Break even = X-P =$100 So if stock price at expiration is $100 you neither make a

profit or a loss.

Case 2

Price of Orange rises to $150 at expiration! (Holder has the right not

OBLIGATION , BUT Writers HAVE OBLIGATION)

Holder does not exercise as they are obligated to sell at $105 and option is

unexercised.

Profit/ loss WRITER

90 95 100 105 110 115 120 125 St

-5

Note: The figure is not drawn to scale!

General Rule for call writers  Profit when X<St

When St>X put holders do not exercise

Max Loss = UNLIMITED

Max Profit = Premium= Profit from the transaction (let us see cartoon example)

• The payoffs of the call holder & writer are MIRROR Images of each

other. My figures are not drawn to scale but still they do look like mirror

images. Similarly, the payoffs of the put holder & writer are MIRROR

Images of each other.

• Also when computing the profit and loss do not forget to take into

consideration the premium paid/received. • Which brings us to a very important point the concept of “Zero sum

game” – all derivatives are "zero-sum" games. That means your gains come

from the losses of others. For instance iff call holder makes a profit of +100,

the call writer will make a loss of -100 ceteris paribus and hence the resulting

sum will equal 0.

•

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

• Intrinsic value of an option This is simply the payoff of a call/put

holder/writer without taking into consideration the premium – Call Option: the difference between the underlying asset’s price and an

option’s exercise price (zero if difference is negative)

– Put Option: the difference between the option’s exercise price and the

underlying asset’s price (zero if difference is negative)

Put call parity

Black-Scholes option pricing model

How does the formula look like Assumptions of the Black-Scholes Option Pricing Model

1. Perfect markets: no transaction costs

2. No default risk premiums

3. Stock does not pay dividends.

4. Continuous trading exists

5. The asset follows stochastic diffusion process

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

THE BLACK-SCHOLES MODEL

)N ()N ( 210 dE edSC R T  

Where

C0 = the value of a call option at time t = 0

R = the risk-free interest rate.

T σ

RES

d 

) 2

()/ln( 2





Tdd  12

N(d) = Probability that a

standardized, normally

distributed, random

variable will be less than

or equal to d.

The Black-Scholes Model allows us to value options in the

real world just as we have done in the 2-state world.

THE BLACK-SCHOLES MODEL: EXAMPLE

Find the value of a six-month call option on a stock with an exercise price of $150

The current value of a share of stock is $160 The interest rate available in the U.S. is R = 5% The option maturity is 6 months (half of a year) The volatility of the underlying asset is 30% per annum

Before we start, note that the intrinsic value of the option is $10—our answer must be at least that amount

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

THE BLACK-SCHOLES MODEL: EXAMPLE (CONTINUED)

Let’s try our hand at using the model. If you have a calculator handy, follow along.

Then,

TσRES d



)5.()/ln( 2

 

First calculate d1 and d2

3 1 6 0 2.05.3 0.05 2 8 1 5.012  Tdd 

52815.0 5.30.0

5).)30.0(5.05(.)150/160ln( 2

1  

d

THE BLACK-SCHOLES MODEL: EXAMPLE (CONCLUDED)

N(d1) = N(0.52815) = 0.7013

N(d2) = N(0.31602) = 0.62401

5 2 8 1 5.01 d

3 1 6 0 2.02 d

)N ()N ( 210 dE edSC R T  

92.20$

62401.01507013.0160$

5.05.



 

• Notice that you only need 5 parameters

1. Current stock price

2. Exercise price

3. Annual risk-free rate, compounded continuously

4. Variance of the continuous return on the stock

5. Time to expiration

This lecture note has been compiled from the slides/chapters/solutions manual that accompanies various editions of a number of books written by RWJ

(Ross et al.) and BMM (Brealey et al.) , Saunders and Cornett and Berk et al.. The definitions, examples are part of the slides/chapters/solutions manual

that accompany the books.

• https://www.optionseducation.org/toolsoptionquotes/optionscalculator

https://www.optionseducation.org/toolsoptionquotes/optionscalculator