Option ( Derivatives)

Muhammad Nowfal S
MSN Institute of Management

A contract (agreement)
Giving a right to buy/ sell
A specific asset
At a specific price
Within a specific time period
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 “An Options contract confers the right but not the obligation to buy
or sell a specified underlying instrument or asset at a specified price
– the Strike or Exercise price, until or at specified future date – the
Expiry date.
 The option buyer has the right and option seller has the obligation
i.e. option buyer may or may not exercise the option given, but, If
option buyer decides to exercise the option, option seller has no
choice but to honour the obligation.
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 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.
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 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.
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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
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 Payoff for buyer of call option
 Payoff for seller of call option
 Payoff for buyer of put option
 Payoff for seller of put option
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 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
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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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 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.
 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 call with a strike of 2250 sold at a
premium of 86.60.
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Nifty closes at Pay off from CE Net Payoff
2100 86.60 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 up-
front 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.
 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
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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

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 As can be seen, as the spot Nifty falls, the put option is in-the-
money.
 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.
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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 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.
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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
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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

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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.
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Position Return Risk
Long Call Unlimited Limited
Short Call Limited Unlimited
Long Put Unlimited Limited
Short Put Limited Unlimited
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 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
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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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Option ( Derivatives)

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