1
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.

2
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

3
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
o
 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.

4
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.
17-19Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
OPTION QUOTES: STRIKE
Strike
Price
Stock
Price
Expiration
17-20Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
OPTION QUOTES: OPTION PRICE
Option Price (cost
would be 100*0.25
= $25 plus
commission)
Change from
previous day

5
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.
17-21Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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
17-22Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
OPTION QUOTES: VOLUME
Volume: Number
of contracts traded
Open Interest:
Number of contracts
outstanding

6
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
20th
!.
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 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
+5
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

7
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 20th! (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
+5
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 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.

8
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 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
+5
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

9
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 20th
!
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
+5
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 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.

10
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

11
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.
17-37Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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

RES
d
)2
()/ln(2
1


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.
17-38Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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 $160The 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

12
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.
17-39Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
THE BLACK-SCHOLES MODEL: EXAMPLE (CONTINUED)
Let’s try our hand at using the model. If you have a calculator handy, follow along.
Then,
T
TσRESd

)5.()/ln( 2
1

First calculate d1 and d2
3 1 6 0 2.05.3 0.05 2 8 1 5.012  Tdd 
52815.05.30.0
5).)30.0(5.05(.)150/160ln( 2
1 
d
17-40Copyright © 2018 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
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$
0
5.05.
0

 
C
eC
• 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

13
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

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