Option
Contract
s
Fortuna Favi et
Fortus Ltd
A contract (agreement)
Giving a right to buy/ sell
A specific asset
At a specific price
Within a specific time
period
2
Buyer of an option: The buyer of an option is the one who by paying
the option premium buys the right but not the obligation to exercise
his option on the seller/writer.
Writer / seller of an option: The writer / seller of a call/put option
is the one who receives the option premium and is thereby obliged
to sell/buy the asset if the buyer exercises on him.
Call option: A call option gives the holder the right but not the
obligation to buy an asset by a certain date for a certain price.
Put option: A put option gives the holder the right but not the
obligation to sell an asset by a certain date for a certain price.
3
Option price/premium: Option price is the price which the option
buyer pays to the option seller. It is also referred to as the option
premium.
Expiration date: The date specified in the options contract is known
as the expiration date, the exercise date, the strike date or the
maturity.
Strike price: The price specified in the options contract is known as
the strike price or the exercise price.
4
Moneyness of a option Contracts
CE
PE
In the money
Spot Price > Strike Price
Spot Price < Strike Price
At the money
Spot price = strike price
Spot Price = Strike Price
Out of the money
Spot Price < Strike Price
Spot Price >Strike Price
Nifty is at 8060
IN THE MONEY
OUT OF THE MONEY
OUT OF THE MONEY
IN THE MONEY
Payoff for buyer of call option
Payoff for seller of call option
Payoff for buyer of put option
Payoff for seller of put option
6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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Rights And Obligations Associated With
Option Positions
Call
Buyer or
Holder
Pays premium to the writer for the right
Writer or
Seller
Receives premium from the buyer and has the
obligation to SELL the underlying asset, if called
upon to do so.
Put
to BUY the underlying asset.
Buyer or
Holder
Pays premium to the writer for the right to
SELL the underlying asset.
Writer or
Seller
Receives premium from the buyer and has the
obligation to BUY the underlying asset, if called
upon to do so.
The profit/loss that the buyer makes on the option depends on the
spot price of the underlying.
If upon expiration, the spot price exceeds the strike price, he makes
a profit. Higher the spot price, more is the profit he makes.
If the spot price of the underlying is less than the strike price, he
lets his option expire un-exercised.
His loss in this case is the premium he paid for buying the option
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• The payoff for the buyer of a three month call option with a
strike of 2250 bought at a premium of 86.60 is as follows
On expiry Nifty closes at
Pay Off from CE
Net Pay Off
2400
150
63.4
2350
100
13.4
2300
50
-36.6
2250
0
-86.6
2200
-86.60
-86.6
2150
-86.60
-86.6
2100
-86.60
-86.6
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6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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If the spot Nifty rises, the call option is in-the-money. If
upon expiration, Nifty closes above the strike of 2250, the
buyer would exercise his option and profit to the extent of
the difference between the Nifty-close and the strike price.
The profits possible on this option are potentially unlimited.
However if Nifty falls below the strike of 2250, he lets
the option expire.
His losses are limited to the extent of the premium he paid
for buying the option.
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For selling the option, the writer of the option charges a premium.
The profit/loss that the buyer makes on the option depends on the
spot price of the underlying.
Whatever is the buyer's profit is the seller's loss. If upon
expiration, the spot price exceeds the strike price, the buyer will
exercise the option on the writer. Hence as the spot price increases
the writer of the option starts making losses. Higher the spot price,
more is the loss he makes.
If upon expiration the spot price of the underlying is less than the
strike price, the buyer lets his option expire un-exercised and the
writer gets to keep the premium.
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The payoff for the writer of a three
month
withPayaoffstrike
sold at a
Nifty closes call
at
from CE of 2250
Net Payoff
2100
86.60
86.60
premium of 86.60.
2150
86.60
86.60
2200
86.60
86.60
2250
86.60
86.60
2300
-50
36.6
2350
-100
13.4
2400
-150
-63.4
2500
-250
-163.4
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As the spot Nifty rises, the call option is in-the-money and the writer starts
making losses.
If upon expiration, Nifty closes above the strike of 2250, the buyer
would exercise his option on the writer who would suffer a loss to the
extent of the difference between the Nifty-close and the strike price.
The loss that can be incurred by the writer of the option is potentially
unlimited, whereas the maximum profit is limited to the extent of the upfront option premium of Rs.86.60 charged by him.
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Put option gives the buyer the right to sell the underlying asset at the
strike price specified in the option.
The profit/loss that the buyer makes on the option depends on
the spot price of the underlying.
If upon expiration, the spot price is below the strike price, he makes
a profit.
Lower the spot price, more is the profit he makes.
If the spot price of the underlying is higher than the strike price, he
lets his option expire un-exercised.
His loss in this case is the premium he paid for buying the option
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the payoff for the buyer of a three month put option (often referred
to as long put) with a strike of 2250 bought at a premium of 61.70
Nifty closes at
Pay off from PE
Net Pay off
2100
150
88.3
2150
100
38.3
2200
50
-11.7
2250
0
-61.70
2300
-61.70
-61.70
2350
-61.70
-61.70
2400
-61.70
-61.70
6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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As can be seen, as the spot Nifty falls, the put option is in-themoney.
If upon expiration, Nifty closes below the strike of 2250, the
buyer would exercise his option and profit to the extent of
the difference between the strike price and Nifty-close.
The profits possible on this option can be as high as the
strike price.
However if Nifty rises above the strike of 2250, he lets
the option expire.
His losses are limited to the extent of the premium he paid
for buying the option.
6/17/2015
Muhammad Nowfal S
MSN Institute of Management
25
For selling the option, the writer of the option charges a
premium.
The profit/loss that the buyer makes on the option
depends on the spot price of the underlying
. Whatever is the buyer's profit is the seller's loss.
If upon expiration, the spot price happens to be below the
strike price, the buyer will exercise the option on the
writer.
If upon expiration the spot price of the underlying is more
than the strike price, the buyer lets his option
un-exercised and the writer gets to keep the premium.
6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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the payoff for the writer of a three month put option (often referred to
as
short put) with a strike of 2250 sold at a premium of 61.70
Nifty closes at
Pay off from PE
Net Pay off
2100
-150
-88.3
2150
-100
-38.33
2200
-50
11.7
2250
0
61.70
2300
61.70
61.70
2350
61.70
61.70
2400
61.70
61.70
6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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As the spot Nifty falls, the put option is in-the-money and the writer starts
making losses.
If upon expiration, Nifty closes below the strike of 2250, the buyer
would exercise his option on the writer who would suffer a loss to the
extent of the difference between the strike price and Nifty close.
The loss that can be incurred by the writer of the option is a maximum
extent of the strike price (Since the worst that can happen is that the asset
price can fall to zero) whereas the maximum profit is limited to the
extent of the up-front option premium of Rs.61.70 charged by him.
6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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Position
Return
Risk
Long Call
Unlimited
Limited
Short Call
Limited
Unlimited
Long Put
Unlimited
Limited
Short Put
Limited
Unlimited
6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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Put Call Parity Model
The prices of European puts and calls on
the same stock with identical exercise
prices and expiration dates have a special
relationship. The put price, call price,
stock price, exercise price, and risk-free
rate are all related by a formula called
put-call parity
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Variable Definitions
C
P
S0
S1
E
R
t
=
=
=
=
=
=
=
call premium
put premium
current stock price
stock price at option expiration
option striking price
riskless interest rate
time until option expiration
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Problem No. 1
Stock of Tata Steel is trading at Rs. 31, Call Option with
Rs.35 Strike Price trading at Rs.8 and put is trading at
12, Expiration for both Call and Put are the same. Bond
worth Rs. 35 on the date of expiry is trading at Rs.30
with Risk free rate. Illustrate Put call Parity.
a. If the stock goes down to Zero
b. Stock Price goes up to Rs.70
Problem No. 2
From the following Information, find out the value of
the Put Option. 3 months Call Option of WIPRO Ltd.
With Strike Price of Rs. 60 trading for Rs.8/-.The
Current Stock Price is Rs. 62/- and Risk free rate of
return is 4% p.a.
Problem No. 3
• You have the following information:
Call price = Rs. 3.5
Put price = Rs. 1
Striking price = Rs. 75
Riskless interest rate = 5%
Time until option expiration = 32 days
what is the equilibrium stock price?
Formula
•
Problem No. 4
• You have the following information:
Spot Price= Rs.120
Call price = Rs. 40
Striking price = Rs. 100
Riskless interest rate = 10% CC
Time until option expiration = 1 Year
what is the Price of Put Option?
Problem No. 5
• You have the following information:
Spot Price= Rs.170
Put price = Rs. 110
Striking price = Rs. 250
Riskless interest rate = 8% CC
Time until option expiration = 6 Months
what is the Price of Call Option?
Black-Scholes
Model
Introduction
❑ A model of price variation over time of financial instruments such as
stocks that can, among other things, be used to determine the price of
a European call option & American option.
❑ The Black Scholes Model is one of the most important concepts in
modern financial theory.
❑ It was developed in 1973 by Fisher Black, Robert Merton and Myron
Scholes and is still widely used today, and regarded as one of the
best ways of determining fair prices of options.
❑ Also known as the Black-Scholes-Merton Model.
Economists
Although Black’s death in 1995 excluded him from the award, Scholes and
Merton won the 1997 Nobel Prize in Economics for their work.
Development and Assumptions
of the Model
●
Derivation from:
– Physics
– Mathematical short cuts
– Arbitrage arguments
●
49
Fischer Black and Myron Scholes
utilized the physics heat transfer
equation to develop the BSOPM
Determinants of the Option
Premium
Striking price
● Time until expiration
● Stock price
● Volatility
● Dividends
● Risk-free interest rate
●
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Striking Price
●
The lower the striking price for a given
stock, the more the option should be
worth
–
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Because a call option lets you buy at
a predetermined striking price
Time Until Expiration
●
The longer the time until expiration,
the more the option is worth
–
52
The option premium increases for more distant
expirations for puts and calls
Stock Price
●
The higher the stock price, the more a
given call option is worth
–
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A call option holder benefits from a rise in the
stock price
Volatility
●
The greater the price volatility, the more
the option is worth
–
The volatility estimate sigma cannot be directly
observed and must be estimated
– Volatility plays a major role in determining time
value
54
Risk-Free Interest Rate
●
The higher the risk-free interest rate, the
higher the option premium, everything
else being equal
–
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A higher “discount rate” means that the call
premium must rise for the put/call parity
equation to hold
Assumptions of the BlackScholes Model
The stock pays no dividends during
the option’s life
● European exercise style
● Markets are efficient
● No transaction costs
● Interest rates remain constant
● Prices are lognormally distributed
●
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Problem No. 1
The Shares of TCL ltd. is currently priced at Rs.415 and
Call option exercisable after 3 months time has a
Exercise price (Strike price) of Rs. 400. Risk Free rate
of Interest is 5% p.a and Standard deviation of share
price is 22%. Calculate the value of call Option based
on the information provided as per the Black & Scholes
Model.
Problem No. 2
The Shares of TCL ltd. is currently priced at Rs.415 and
Call option exercisable after 3 months time has a
Exercise price (Strike price) of Rs. 400. Risk Free rate
of Interest is 5% p.a and Standard deviation of share
price is 22%. Calculate the value of call Option based
on the information provided as per the Black & Scholes
Model.
Problem No. 2
The Shares of Infy ltd. is currently priced at Rs.90 and
Call option exercisable after 6 months time has a
Exercise price (Strike price) of Rs. 80. Risk Free rate of
Interest is 8% p.a and Standard deviation of share price
is 23%. Calculate the value of call Option based on the
information provided as per the Black & Scholes
Model.
The model most commonly used by a practitioners and traders to
price and value options is the Black-Scholes pricing model. The
Black-Scholes model examines five factors that affect the price of
an option:
1. The spot price of the underlying asset
2. The exercise price on the option
3. The option’s exercise date
4. Price volatility of the underlying asset
5. The risk free rate of interest
6/17/2015
Muhammad Nowfal S
MSN Institute of Management
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The difference between the underlying asset’s spot price and an
option’s exercise price is called the option’s intrinsic value.
Intrinsic value means how much is option ITM. Deeper is the option
in the money more is the intrinsic value of an option. If the option is
OTM or ATM its intrinsic value is zero.
For a call option intrinsic value is
Max (0, (St – K)) and
For a put option intrinsic value is
Max (0, (K - St))
(Where, St - Stock Price K - Strike Price)
In other words Intrinsic value can only be positive or zero.
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Time Value of an option: Time value is difference between option
premium and intrinsic value. It comprises of
1. Risk free rate
2. Volatility
3. Time to Expiry
The time value of an option is always positive and declines
exponentially with time, reaching zero at the expiration date. At
expiration, where the option value is simply its intrinsic value, time
value is zero.
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Settlement in Options
Contracts
Options P&L for the buyer
Different Scenarios
• Call and Put option Long, close before the
expiry (BUYER)
• Call and Put option short, close before the
expiry (SELLER)
• Call option, Long, held to expiry
• Call option short, held to expiry
• Put option, Long, held to expiry
• Put option short, held to expiry
Eg.
Let us change the example from Reliance to TCS, to
break the monotony
Here are the trade details –
• Underlying = TCS
• Strike = 3520
• Premium = 55
• Option type = Put
• Position = long
• Settlement price = 3390
• Lot Size: 250
Option Greeks
Delta of an Option
Theta of an Option
Vega