Options.pptx

“Options” Derivatives
Course: “Financial Derivatives

 Outline
1. Background
2. Definition
3. Option and Future Dissimilarities
4. Option and Future Similarities
5. Basic Terms of Option
6. Hedging Risk bidirectionally
7. Types of Option
“Outline”----Options Derivatives

8. Exercising Styles of Option
9. Positions in Option
10. “Bearish-to-Neutral-to-Bullish” views about
the Market movement
11. Moneyness of Option
12. Option Payoffs vs. Option Profit
13. Option Profit and Breakeven
14. Graph Of Call and Put Option
15. Kinship of Option
16. Pricing of Option
“Outline”----Options Derivatives

Background
 As the Futures Contracts are useful in
Hedging risks related to the Price
movements of the Underlying shares, they
hedge the Risk only in one direction and
one can still suffer a large loss in the other
direction.
 So Options were introduced that consists
of mechanisms that help eliminate the risk
on an underlying asset much more
effectively.

What is an option?
(Definition)
 An Option is a financial Instrument that
provides the holder with the right without
obligation to buy or sell a specified
quantity of an underlying asset at a fixed
price (called a strike price or an exercise
price) at or before the expiration date of
the option.
 Since it is a right and not an obligation,
the holder can choose not to exercise the
right and allow the option to expire.

Options Versus Futures
 The major difference between options and
Futures arise from the phrase “without
Obligation”
 i.e., the holder of an option need not to
exercise his right if the price movement of
the underlying asset is adverse, the holder
of a future contract has to honor the
contract even if it means incurring a loss.

 Due to “without obligation” feature of
Option Derivatives, the price (which is
known as Premium) of Option is much
higher than the price of a comparable
Future Contract as nothing in the world is
free.
Options Versus Futures

Option and Future Similarities
 Like Futures Contract, Options Contracts
too are derived from an underlying asset,
which could be a Financial security
(shares, indices, bonds/debentures,
T.Bills, etc.), a commodity or index.
 Like Futures, Options are traded in an
active secondary market

Basics Concepts/Terms Of
Options
 Options are a separate instruments from the
Stocks
 Options are created on an “underlying asset”
 If there is no underlying asset, there is no option
 There must be price uncertainty (price volatility)
 Options must have an “expiry date” (due date)
 Option Exercise price is called “strike price”

Basics Concepts/Terms
(Buyers and Writers of Option)
 For every option there is both a buyer and
a writer
 Seller is called “Option writer”
 Buyer is called “Option Holder”
 The buyer pays the writer for the ability to
choose when to exercise, the writer must
abide by buyer’s choice
 Buyer puts up no margin while writer must
post margin

 Options vest the RIGHT(without
obligation) only upon the BUYER of the
CALL or PUT OPTION and not upon the
Writer/Seller of the Option.
 If the buyers of the Option decide to
exercise their right, the writers are
obliged to honor their commitments.
Basics Concepts/Terms
(Buyers and Writers of Option)

Terms of Options Contract
 T = Exercise date
 X or K = Exercise price OR Strike Price
 C = Option Premium is the price paid by
the option holder to buy the option
 Underlying Asset such as shares,
indices, bonds, debentures, T-Bills, etc.,
 ST = Market Price of Underlying Asset

Options –Hedging of Risk in Two
Directions
 Options provide investors with the
opportunity to insure the risk arising
from Price Fluctuations
 “How can one insure oneself against the
fall in price and yet avail the benefit of a
price rise?”

 Assume that one has 4000 shares priced
at Rs. 240 each to start with. One can buy
an option that gives the right (without
obligation) to sell 4000 shares at Rs. 250
each (called exercise price or strike price)
three months later. Naturally one pays a
price for this option. Suppose the option to
sell 4000 shares at Rs. 250 each, three
months from now costs Rs. 16000. This is
also known as Option Premium.
Directions

 If Price Rises
 If three months later the market price of
the share is for example Rs. 260, one may
decide not to exercise the option as the
shares can now be sold in the market at
Rs. 260 each, for a total cost of Rs.
10,40,000. Even after deducting Rs.
16,000 towards the option price there is
still a gain of Rs. 24000.
Directions

If Price Falls
If on the other hand, three months later the price
falls to Rs. 230, one can exercise the Option to sell
the shares at Rs. 250 each , thereby avoiding the
possible loss of Rs. 80,000 which one would have
suffered if one had not purchased the Option .
Thus for a premium of Rs. 16,000 one has
effectively insured oneself against all
possible losses arising during the three
months
Directions

 Call Option (a right to buy)
 Put Option (a right to sell)
Two Basic Kinds of Options

 A Call Option confers the Right to BUY
the underlying asset, at a specified price
on or before a certain date in the future
 A Put Option confers the Right to SELL
the underlying asset, at a specified price
on or before a certain date in the future.
Two Basic Kinds of Options

Example of Call Option
One buy 2000 shares at Rs. 150 (Exercise
Price or Strike Price ) at an option
premium or call premium e.g. Rs. 4000.
If the price of the share three months later
rises to Rs. 160, one can exercise the
option to buy the shares at Rs. 150. Thus
there is a gain of Rs. 16,000 ( Rs. 20,000
profits-Rs. 4000 of premium paid).

 If on the other hand, the price falls to e.g.,
130, one would not exercise the option
and invest at the lower prevailing price,
thus gaining Rs.36000 (Rs. 40,000 saved
on the lower price – Premium paid of Rs.
4000).
 Thus one would have covered ones risk in
either direction
Example of Call Option

Option’s Exercise Styles
(American Option Vs. European)
 If the right can be exercised anytime within
a specified period then the Option is
known as an American Option.
 If the right can be exercised only on a
specific date then the Option is known as
an European Option.

 By purchasing the Call Option, one takes the
Long Call Position and is called the Long Call
Holder,
 Similarly the Counter-party who sold these
Call Options has the Short Call position and is
the Call Writer
 Since long and short positions of an option are
opposite counter-parts to each other, the gains
of a long position holder are the losses of
the short position holder and vice versa
Positions in Options

Positions in Options
 Four Possible Positions can be taken in Option
Derivatives;
1. Long Call Position taken by Call Holder/Buyer
2. Short Call Position taken by Call Writer/Seller
3. Long Put Position taken by Put Holder/Buyer
4. Short Put Position taken by Put Writer/Seller

Views about the Market
movements
 It is important to understand,
 “Why anyone would wish
to buy or sell either
Put or Call Option?”

 Buying or Selling of Put and Call Options
indicates the buyer or seller’s View
regarding the future market price
movement of the underlying asset.
 At any given point in time there could be
Bearish-to-Neutral-to-Bullish views
about the Market movement
Movement

 The level of confidence in ones view of
the market movement determines the
position one takes.
 Whatever may be one view, in order for
the trade to materialize there has to be
somebody who has an equally confident
but opposite view of the market
Movement

 Buying a Call/Long Call position indicates
that you are BULLISH about the market
while the counter party (short call position)
has Bearish view about the market.
 Buying a Put/Long Put position indicates
that you are BEARISH view about the
market
Movement

FOUR OPTIONS
• Sell a Put option
• Outlook bullish/
Neutral
• Opposite of short
calls / long puts
• Sell a Call
option
• Outlook Bearish
or Neutral
• Opposite of long
calls/ short puts
• Buy a Put option
• Outlook Bearish
• Opposite of long
calls and short
Puts
• Buy a call option
• Outlook bullish
• Opposite of short
calls and long
put
LONG
CALLS
LONG
PUTS
SHORT
PUTS
SHORT
CALLS

Moneyness of Option
An important aspect related to the Options is the
relationship between the Spot price of Underlying
asset and the Exercise Price of Option.
Moneyness is the relative position of the current
price (or future price) of an underlying asset (e.g., a
stock) with respect to the strike price of a derivative
So there have three conditions,
 At-the-money option (ATM)
 In-the-money option (ITM)
 Out-of-the-money option (OTM)

 At The Money (ATM): An Option is an
ATM Option when strike price is same as
current spot price [X = ST], so the decision
to exercise becomes irrelevant.
 In The Money (ITM): when two prices are
such that it is profitable for the Option
holder to exercise the option.
 Out of The Money (OTM): when it is better
for the holder not to exercise the option.
Moneyness of Option

Call Option Put Option
ATM
X = ST X = ST
ITM
X < ST X > ST
OTM
X > ST X < ST
Call and Put Moneyness Terms

15-32
Option “Moneyness”
 Summarizing
In-the-
Money
Out-of-the-
Money
Call
Option
S > K S ≤ K
Put Option S < K S ≥ K

Call Option Moneyness Terms
 At The Money (ATM): when strike price is same as
current spot price [X = ST] and payoff from exercising
is zero
 In The Money (ITM): A Call Option will be ITM when
strike price is below the current spot price [X < ST] and
the payoff from exercising is positive i.e., (St–X) > 0
 Out of The Money (OTM): A Call Option will be OTM
when the strike price is above the current spot price
[X > ST] and the payoff from exercising is zero
i.e., (St–X) < 0 so no reason to exercise

15-35
Option Payoffs versus Option Profits
Option investment strategies involve initial and terminal cash
flows.
 Initial cash flow:- option price (often called the option
premium).
 Terminal cash flow:- the value of an option at expiration
(often called the option payoff ).
 The terminal cash flow can be realized by the option holder
by exercising the option.
 Option Profits = Terminal cash flow − Initial cash flow
OR
 Option Profits = Option Payoff− Option Premium

 Long Call Option Profit
= Long Call Option Pay Off (in the Money) – Option Premium
= (St–X) – Option Premium
 Long Put Option Profit
= Long Put Option Pay Off (in the Money) – Option Premium
= (X–St) – Option Premium

 Since long and short positions of an option
are opposite counter-parts to each other,
the gains of a long position holder are
the losses of the short position holder
and vice versa

 Let us assume that one buys a European
Call Option maturing 30 days from today
on a certain stock. Assume that strike price
is Rs. 125 and the Call Premium is Rs. 10.
This is also the Premium Income for the
Call Writer/ Short Call Holder. On 30th day,
if the underlying share price is for example
Rs.140, what are the payoffs for a Long
and Short Call?
An Example of Call Option

 Solution
 T = Exercise date = 30th
 X or K = Exercise price OR Strike Price = Rs. 125
 C = Call Premium = Rs. 10
 ST = S30 = Market Price at 30th day = Rs. 140

 Call Option Profits = Call Payoff− Option Premium
 Call Option Profit = (St–X) – Option Premium
 Call Option Profit = (140–125) – 10
 Call Option Profit = (15) – 10
 Call Option Profit = Rs.5
(Note:- If Rs.5 is Long Call Option Profit, then at the
same time Rs. 5 is Short Call Option Loss)

 One must remember that actual benefit on the
contract only occurs when the underlying share
price moves beyond the Breakeven Level
 Call Option Breakeven = (Strike + Premium)
 Call Option Profit = St - Call Option Breakeven
 Put Option Breakeven = Strike – Premium
 Put Option Profit = Put Option Breakeven – St
“Option Profits and Breakeven”

 Call Option Profit occurs if
 ST > Call Option Breakeven
 S30 > (Strike + Premium)
140 > (125 + 10)
140 > 135
 As the above condition is fulfilled so Call
Option is at Profit
 Call Option Profit = ST - Call Option Breakeven
 = 140 – 135
 = Rs. 5
“Option Profits and Breakeven”

Summary of Call vs Put
Call Options
 Right to buy
 Bullish position
 Breakeven = Strike +
Premium
 Stock must move up
for profitable option
 ITM when stock price >
strike price
Put Option
 Right to sell
 Bearish position
 Breakeven = Strike –
Premium
 Stock must move down
to be profitable
 ITM when strike price
< stock price

Convertible Debentures & Call
Options Kinship
 Convertible Debentures is simply an
Option to purchase a given number of
shares in exchange for the Value of
Debenture (akin to exercise price)
 Dissimilarity includes;-
Unlike an Option, Convertible Bond has an
independent existence of its own and is useful
in mobilizing funds in the Primary Market.

 Warrants are frequently used as
sweetener by the corporate while selling
their public issues.
 A share Warrant also involves an option of
purchasing a given number of Equity
shares by paying a predetermined
Exercise Price
Warrants & Call Options Kinship

Warrants
(continued)
 The issuer settles up with the holder
when a warrant is exercised
 When call warrants are issued by a
corporation on its own stock,
exercise will usually lead to new
treasury stock being issued

Employee Stock Options
 Employee stock options are a form of
remuneration issued by a company to its
executives
 They are usually at the money when issued
 When options are exercised the company issues
more stock and sells it to the option holder for
the strike price
 Expensed on the income statement

“How are Option Premium Priced ?”
Option Pricing

I. Boundary Conditions
II. Minimum & Maximum Values
III. Lower Bounds
IV. The Variables affecting the Option premium
(B) Models of Option Premium
Option Pricing
(A) Principles of Options Pricing:

1. Principles of Options Pricing
I. Boundary Conditions

 The minimum value of any option is zero. We state
this formally as:
Co > O, Po > O
 No option can sell for less than zero, for in that case
the writer would have to pay the buyer.
 Now consider the maximum value of an option.
 It differs somewhat depending on whether the option
is a call or a put and whether it is European or
American.
 The maximum value of a call is the current value of
the underlying: Co < So
 A call is a means of buying the underlying. It would
not make sense to pay more for the right to buy the
underlying than the value of the underlying itself.
II. Minimum & Maximum Values

 For a put, it makes a difference whether the put
is European or American.
 One way to see the maximum value for puts is
to consider the best possible outcome for the
put holder.
 The best outcome is that the underlying goes to
a value of zero. Then the put holder could sell a
worthless asset for X.
 For an American put, the holder could sell it
immediately and capture a value of X.
 The maximum value of an American put is the
exercise price,
Po < X
Cont…

 Fortunately, we can tighten the range up a
little on the low side: We can establish a
lower bound on the option price.
 For American options, which are exercisable
immediately, we can state that the lower
bound of an American option price is its
current intrinsic value:
III. Lower Bounds

IV-“Variables affecting the
Option Premium”
 Time to Expiry
 Volatility of Underlying Asset Price
 Current short term interest rate
 Dividends to be paid in the underlying
share

Variables affecting the Option
Premium
 Time to Expiry:
 Option prices are affected by the time to
expiration of the option
 lesser the time to expiry ,lesser the time value of an
option and lesser the price of the option and vice
versa
 A longer term option has more time for the
underlying to make a favorable move
 Volatility of Underlying Asset Price
 High beta stocks are more volatile and so they
are highly priced and vice versa

Premium
 Current short term interest rate
 Short term interest rate also affects the
Option Premium because premium paid has
an opportunity cost in terms of time value. In
other words if one did not buy an option, one
could have earned some interest on the
premium amount by investing it in a risk-free
opportunity.
 So higher the rate of interest, higher is the
opportunity loss of buying an option and

Premium
share
 If the underlying asset is likely to pay out
dividends during the period of option, this will
also affect the premium. This is because
when a company declares a dividend its
market price falls ex-dividend, thus impacting
the underlying share price.

share
When market price falls, it reduces
the benefit to call holder while increasing
the benefit to a put holder
To compensate for this loss or gain, the
call option premium reduces, while the put
option premium increases
Premium

“Models of Option Premium”
 There are two different models for valuing
the two kinds of Options:
1) Black-Scholes Option Pricing formula for
pricing the European Options
2) Binomial Tree Model (also called Lattice
Approach) for pricing the American
Options

The Black-Scholes-Merton
Formula
 Black-Scholes approach forms the core of
much of Option pricing. This formula was
initially developed by Fisher Black and
Myron Scholes, Robert Merton
contributed significantly to its later
development.
 What the model does is to price a
European call on non-dividend paying
stock.

Assumptions of the Model
1) The stock prices are assumed to follow a
random walk, just as gas particles in a
closed chamber do. This means that the
proportional change in stock prices in a
brief period of time follow a normal
distribution. This is the same as saying
“Underlying Stock Prices follow a log-
normal probability distribution”
For example, if a stock moves from 100 to
110, the return is 10 percent but the log
return is ln(l.lO) = 0.0953 or 9.53 percent.

Assumptions of the Model
2) The volatility (standard deviation) of stock
price is denoted by σ
3) Securities may be short sold with access to
full proceeds without any transaction cost
4) The stock pays no dividend during the life
of option
5) The risk free rate of interest r is constant
and remains the same for all maturities
6) The market is efficient and hence arbitrage
opportunities are virtually absent

 The Black-Scholes-Merton formulae for
the prices of call and put options are:
 d2 = dl - σ√T
Model

Where,
 So is the price of the underlying,
 X is the exercise price,
 rC is the continuously compounded risk-free
rate,
 T is the time to expiration.
 σ is the standard deviation of the log return on
the asset and it depicts the volatility of stock
Formula

 e=2.7182
 N(dl) and N(d2) represent normal
probabilities based on the values of dl and
d2.
 Normal probability table is used after
computing the values for dl and d2 from
formula
Formula

 Consider the following example. The underlying
price is 52.75 and has a volatility of 0.35. The
continuously compounded risk-free rate is 4.88
percent.
 The option expires in nine months; therefore, T
= 9/12 = 0.75. The exercise price is 50.
 First we calculate the values of dl and d2:
Example

The Binomial Model
 The word "binomial“ refers to the fact
that there are only two outcomes.
 In other words, we let the underlying price
move to only one of two possible new
prices.
 We let S be the current underlying price.
One period later, it can move up to S+ or
down to S-.
 We let X be the exercise price of the
option and r be the one period risk-free

 So that u and d represent 1 plus the rate of return
if the underlying goes up and down, respectively.
 Thus, S+ = Su and S- = Sd.

Example
 If shares of a company are currently
quoting at Rs. 130 each. Let us assume
that the prices of theshare three months
from now is expected to be either Rs.
143.67 or Rs. 117.63 per share. If exercise
price is Rs. 140, three months to
expiration, Risk free rate is 6%, σ= 0.20,
What would be the Price of European call
option?

uS=143.67
C3 = 3.67
dS = 117.63
C3 = 0
T = 0
u = 1.1052
d = 0.9048
p = 0.5505
P=55.05%
(1-p)= 44.95%
T = 3 months

 The expected value of call option at the
end of three months is Rs. 2.023
 (=0.5505 * 3.67 + 0.4495* 0)

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