CHAPTER 7
OPTIONS AND THEIR VALUATION
LEARNING OBJECTIVES
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 Explain
the meaning of the term option
 Describe the types of options
 Discuss the implications of combinations of
options
 Highlight the factors that have an influence on the
valuation of options
 Develop a simple model of valuing options
 Show how the Black-Scholes model of option
valuation works
Options
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 An
option is a contract that gives the holder a right,
without any obligation, to buy or sell an asset at an
agreed price on or before a specified period of time.
 The
option to buy an asset is known as a call
option.
 The
option to sell an asset is called a put option.
Options
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 The
price at which option can be exercised is called
an exercise price or a strike price.
 The
asset on which the put or call option is created
is referred to as the underlying asset.
When an Option can be Exercised
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 European
option When an option is allowed to be
exercised only on the maturity date, it is called a
European option.
 American
option When the option can be exercised
any time before its maturity, it is called an American
option.
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Possibilities of option holder exercising his
right
There are three possibilities:
 In-the-money: A put or a call option is said to in- the- money
when it is advantageous for the investor to exercise it.
 Out-of-the-money: A put or a call option is out-of-the-money
if it is not advantageous for the investor to exercise it.
 At-the-money: When the holder of a put or a call option does
not lose or gain whether or not he exercises his option, the
option is said to be at-the- money.
Call Option
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 Buy a call option
 You should exercise call option when:
•

Do not exercise call option when:
•

Share price at expiration < Exercise price.
The value of the call option at expiration is:
•

Share price at expiration > Exercise price.
Value of call option at expiration = Maximum [Share price –
Exercise price, 0].
The expression above indicates that the value of a call
option at expiration is the maximum of the share price
minus the exercise price or zero.
 The
call buyer’s gain is call seller’s loss.
Pay-off of a call option buyer
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Pay-off of a call option writer
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Call Premium
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 The
buyer of a call option must, pay an up-front
price, called call premium, to the call seller to buy
the option.
 The
call premium is a cost to the option buyer and
a gain to the call seller.
Example: Call Option Pay-off
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 The
share of Telco is selling for Rs 104. Radhey
Acharya buys a 3 months call option at a premium
of Rs 5. The exercise price is Rs 105. What is
Radhey’s pay-off if the share price is Rs 100, or Rs
105, or Rs 110, or Rs 115, or Rs 120 at the time the
option is exercised?
Example : Pay-off of the call option buyer
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The Call Option Holder's Pay-off at
Expiration
Pay-off of the call option buyer
Example: Pay-off of the call option seller
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The Call Option Seller's Pay-off at
Expiration
Pay-off of the call option seller
Put Option
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 Buy a put option
 Exercise the put option when:
•

Do not exercise the put option when:
•

Exercise price > Share price at expiration.
Exercise price < Share price at expiration.
The value or payoff of a put option at expiration will be:
•
 The
Value of put option at expiration = Maximum
Share price at expiration, 0].
[Exercise price –
put option buyer’s gain is the seller’s loss.
Example : Put Option Pay off
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investor hopes that the price of BHEL’s share will fall after
three months. Therefore, he purchases a put option on BHEL’s
share with a maturity of three months at a premium of Rs 5.
The exercise price is Rs 30. The current market price of
BHEL’s share is Rs 28. How much is profit or loss of the put
buyer and the put seller if the price of the share at the time of
the maturity of the option turns out to be Rs 18, or Rs 25, or
Rs 28, or Rs 30, or Rs 40?
 An
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Example
The Put Option Holder's Pay-off at
Expiration
Pay-off for a put option buyer
Example
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The Put Option Seller's Pay-off at
Expiration
Pay-off for the put option seller
Options Trading in India
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 The
Security Exchange Board of India (SEBI) has
announced a list of 31 shares for the stock-based
option trading from July 2002. SEBI selected these
shares for option trading on the basis of the following
criteria:
Shares must be among the top 200 in terms of market
capitalisation and trading volume.
Shares must be traded in at least 90 per cent of the trading
days.
Options Trading in India
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The non-promoter holding should be at least 30 per cent and
the market capitalisation of free-float shares should be Rs 750
crore.
The six-month average trading volume in the share in the
underlying cash market should be a minimum of Rs 5 crore.
The ratio of daily volatility of the share vis-à-vis the daily
volatility of the index should not be more than four times at
any time during the previous six months.
Options Trading in India
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The minimum size of the contract is Rs 2 lakh. For the first six
months, there would be cash settlement in options contracts
and afterwards, there would be physical settlement. The
option sellers will have to pay the margin, but the buyers will
have to only pay the premium in advance. The stock
exchanges can set limits on exercise price.
Index Options
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 Index
options are call or put options on the stock
market indices.
 In
India, there are options on the Bombay Stock
Exchange (BSE)—Sensex and the National Stock
Exchange (NSE)—Nifty.
Index Options
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 The
Sensex options are European-type options and expire on
the last Thursday of the contract month. The put and call index
option contracts with 1-month, 2-month and 3-month maturity
are available. The settlement is done in cash on a T + 1 basis
and the prices are based on expiration price as may be decided
by the Exchange. Option contracts will have a multiplier of
100.
 The
multiplier for the NSE Nifty Options is 200 with a
minimum price change of Rs 10 (200  0.05).
Combinations of Put, Call and Share
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A
share, a put and a call can be combined together
to create several pay-off opportunities. Some of
these combinations have significant implications.
They are:

Long Position: A long position involves buying and
holding shares (or any other assets) to benefit from
capital gains and dividend. An investor may create a
long position in the shares of a firm. A long position
investment strategy is risky. The investor will incur
loss if the share price declines.
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Example

Suppose the current share price and the exercise
price to be Rs 100, and possible share prices at
expiration Rs 90 or Rs 110. The pay-off (value)
of a portfolio of a share (long) and a put (long) at
expiration is
Value of share
Current share
price
Share price
Protective Put
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Put option at-the-money is called a protective put
.The combination of a long position in the share
and a protective put helps to avoid the investor’s
risk when the share price falls.
Va lue of share
a nd put
Curre nt share
price
Exerci se pric e
Share price
Protective Put vs. Call
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 The
value of your portfolio of a share and a put at
expiration will always be greater than the value of a
call at expiration by the exercise price.
 At
expiration, the position will be as follows:
Share price at expiration + Value of put at expiration = Value
of call at expiration + Exercise price
Protective Put vs. Call
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Put-call Parity
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
Suppose you buy a share (long position), buy a put (long position) and sell
a call (short). The current share price is Rs 100 and the exercise price of
put and call options is the same, that is, Rs 100. Both put and call options
are European type options and they will expire after three months. Let us
further assume that there are two possible share prices after three months:
Rs 110 or Rs 90. What is the value of your portfolio?
Value of a Portfolio of a Share and a Put Option
Covered Call
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 Naked
option is a position where the option writer does not
hold a share in her portfolio that has a counterbalancing effect.
 A covered
call position is an investment in a share plus the
sale of a call on that share. The position is covered because the
investor holds a share against a possible obligation to deliver
the share. The total value or pay-off of a covered call at
expiration is the share price minus the value (pay-off) of the
call.
Pay off of a covered call
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Combinations of Put, Call and Share
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 Straddle:
Combining Call and Put at Same
Exercise Price
 Strips and Straps
 Strangle: Combining Call and Put at Different
Exercise Prices
 Spread: Combining Put and Call at Different
Exercise Prices
 Spread: Combining the Long and Short Options
 Collars
Pay offs : Straddle
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Straddle Buyer
Straddle Seller
Pay offs: Strips and Straps
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Strips
Straps
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Strangle: Combining Call and Put at Different
Exercise Prices
 A strangle
is a portfolio of a put and a call with the
same expiration date but with different exercise
prices. The investor will combine an out-of-themoney call with an out-of-the-money put.
Example
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 Suppose
the Telco share is currently selling for Rs 110. The
exercise prices for the Telco put and call are, respectively,
Rs 100 and Rs 105. What will be your pay-off if the price
of Telco’s share increases to Rs 120 in three months?
 You will forgo put option, but you will exercise call option.
So your pay-off will be the excess of the share price over
the call exercise price: Rs 120 – Rs 105 = Rs 15.
 If Telco’s share price falls to Rs 95, you will exercise put
option and pay-off will be the excess of exercise price over
the share price: Rs 100 – Rs 95 = Rs 5.
Payoff from Strangle
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