Muhammad Nowfal S

MSN Institute of Management

OPTIONS

Meaning

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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Key Terms 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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Option pay offs

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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Payoff for buyer of call 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 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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An example • 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 Off2400 150 63.42350 100 13.42300 50 -36.62250 0 -86.62200 -86.60 -86.62150 -86.60 -86.62100 -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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Payoff profile for writer of call options

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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An example

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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MSN Institute of Management

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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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Payoff profile for buyer of put options

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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An example 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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payoff profile for writer of put options:

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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An example 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 -38.332200 -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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OPTION VALUES

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 asset2. The exercise price on the option

3. The option’s exercise date4. Price volatility of the underlying asset

5. The risk free rate of interest

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Intrinsic value

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 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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