Derivatives Options

8/4/2019 Derivatives Options

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An option gives you the right, but not the obligation to either

buy (Call Option) or sell (Put Option) an asset at a certain price

(known as the strike) on a certain date. For this right to buy or

sell the underlying asset, you pay a premium upfront to the

seller of the option. Whether you choose to use, or exercise, thisright, is dependent upon the market conditions at the time the

option expires.

What is an option


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Underlying - The specific security / asset on which an options contract is based

Option Premium - This is the price paid by the buyer to the seller to acquire the right

to buy or sell

Strike Price or Exercise Price - The strike or exercise price of an option is the specified/

pre-determined price of the underlying asset at which the same can be bought or soldif the option buyer exercises his right to buy/ sell on or before the expiration day

Expiration date - The date on which the option expires is known as Expiration Date.

On Expiration date, either the option is exercised or it expires worthless

Exercise Date - is the date on which the option is actually exercised. In case ofEuropean Options the exercise date is same as the expiration date while in case of

American Options, the options contract may be exercised any day between the

purchase of the contract and its expiration date (see European/ American Option)

Important Terminology


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Open Interest - The total number of options contracts outstanding in the market atany given point of time

Option Holder: is the one who buys an option which can be a call or a put option. He

enjoys the right to buy or sell the underlying asset at a specified price on or before

specified time. His upside potential is unlimited while losses are limited to the

Premium paid by him to the option writer

Option seller/ writer: is the one who is obligated to buy (in case of Put option) or to

sell (in case of call option), the underlying asset in case the buyer of the option

decides to exercise his option. His profits are limited to the premium received from

the buyer while his downside is unlimited

Option Class: All listed options of a particular type (i.e., call or put) on a particular

underlying instrument, e.g., all Sensex Call Options (or) all Sensex Put Options

Important Terminology (Contd)


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An American style option is the one which can be exercised by the buyer on or

before the expiration date, i.e. anytime between the day of purchase of the option

and the day of its expiry

The European kind of option is the one which can be exercised by the buyer on the

expiration day only & not anytime before that

American & European Options


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An option is said to be at-the-money, when the option's strike price is equal to

the underlying asset price. This is true for both puts and calls

A call option is said to be in-the-money when the strike price of the option is less

than the underlying asset price. For example, a Sensex call option with strike of

3900 is in-the-money, when the spot Sensex is at 4100 as the call option hasvalue. The call holder has the right to buy a Sensex at 3900, no matter how much

the spot market price has risen. And with the current price at 4100, a profit can be

made by selling Sensex at this higher price

On the other hand, a call option is out-of-the-money when the strike price is

greater than the underlying asset price. Using the earlier example of Sensex calloption, if the Sensex falls to 3700, the call option no longer has positive exercise

value. The call holder will not exercise the option to buy Sensex at 3900 when the

current price is at 3700

At the Money, In the Money, Out of the Money


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CALL OPTION PUT OPTIONIn-the-money Strike price < Spot price of

underlying asset Strike price > Spot price ofunderlying assetAt-the-money Strike price = Spot price of

underlying asset Strike price = Spot price ofunderlying asset

Out-of-the-money Strike price > Spot price ofunderlying asset Strike price < Spot price ofunderlying asset

At the Money, In the Money, Out of the Money


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You expect the Dollar to strengthen against the

Rupee. The Current Rate is 44.0000

You Buy the 1 month USD/INR call option at a strike

of 44.0100 You pay a premium of Rs. 90 for the option on $1000

On expiry the price is at 44.6000

Profit = 44.6000-44.0100 - .09 = 0.5 You make a profit of Rs. 500 on the trade of $1000

A Trading Scenario


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All Payoff Diagrams


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Intrinsic Value

Price of the underlying asset minus the strike of the option as the option's

intrinsic value (for a Call option, for a Put it is just the opposite)

Time Value

The amount by which the value of the option exceeds the intrinsic value.

The volatility of the underlying asset has a significant bearing on the time value. Time

value increases as volatility increases because of the Profit/Loss scenario for an option.

An option on an asset which is more likely to take on extreme values is much more

valuable than on a less volatile asset.

Interest rates differentials in the two currencies involved in a currency option trade must

also be taken into consideration when pricing an option, and these are also a function of

time.

Pricing of Option


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Pricing Illustrated


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Let's say that you hold a Call option with a 44.2000 strike price, and that

the market price of USD/INR has risen to 44.2155. Your option is worth

225 pips thirty days before the option's expiration date. The intrinsic value

is the difference between the strike price for the underlying asset in the

option contract (44.2000) and the market price (44.2155). If you hold a call

option, which gives you the right to buy USD/INR at 44.2000 and themarket price is 44.2155 the intrinsic value of the option is 155 pips. So the

price of the option is the intrinsic value plus the time value (in this case 70

pips).

Example


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You can limit your risks (maximum potential loss is the premium if you are

the buyer) and you will still have unlimited profit potential.

Options require less money up front than if, for example, you take a

regular spot position. This is because you don't buy the asset itself but

only a contract that gives you the right to either buy or sell the asset at a

given price. Therefore, if you are the buyer, you will only have to pay the

premium upfront. On the other hand, if you are the seller of an option,

you receive the premium upfront, but then you have the possibility of an

unlimited loss.

An option offers you some important hedging opportunities.

Why Options


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SCENARIO You want to capitalize on an increasing trend in the spot market. The trend could be either short or long term.

ACTION Buy Call with strike A (see Long Call graph). Any strike price is bullish, however, the higher you set the strike , the more

out-of-the-money the option is, thus the higher the leverage.

Long Call


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You believe USD/INR will rise towards the 47.22 level in about a month's

time. The spot is currently 47.1720. You buy USD/INR Call for one month

with a strike of 47.1750. The price is 108 pips.

UPSIDE

The profit region for this option is any spot price above 47.1858(the option's break-even

point) and is potentially unlimited.

DOWNSIDE

The risk is limited to the cost of the premium (108 pips), which will be lost if the options

are worthless at the time of expiry.

Example Long Call


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SCENARIO

You expect minor changes in the spot, and these will more than likely result in a decrease in the spot. You can also use

this strategy if you believe that the option is priced too high, i.e. the market expects the price to move more than you

think it will.

ACTION

Sell Call with strike A (See Short Call graph). Any strike price you select should be bearish, reflecting your view of how

the currency will perform over the period of the option.

Short Call


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EXAMPLE

You expect USD/INR to remain fairly stable at the current market levels for the next

month. The spot is 47.1720. You sell a USD/INR Call with a strike of 47.18 for a premium

of 86 pips.

UPSIDE

This strategy's profit potential is the premium received, 86 pips.

DOWNSIDE

The risk region for this strategy is any price above 47.1886 at the time the option

expires.

Example Short Call


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SCENARIO

You anticipate a large move in the spot, perhaps in connection with a certain event, but you are not

sure of the direction of the move.

ACTION

Buy a Put and a Call with the same strike price. The strike price should be roughly at-the-money

(equal or nearly equal to the market price).

Long Straddle


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EXAMPLE

You believe that USD/INR will move significantly in either direction in the next month. The spot is

47.1730 and the forward price is app. 47.1750. You buy a USD/INR Call and a USD/INR Put for one

month with a strike of 47.1750 for a premium of 128 pips and 127 pips, respectively. The total

premium is 255 pips.

UPSIDE

The profit region is any price above 47.2005 or below 47.1495.

DOWNSIDE

The risk is limited to the cost of the premiums (255 pips), which will be lost if the options are

worthless at the time of expiry.

Example Long Straddle


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SCENARIO

You anticipate a large move in the spot, in either direction, if the spot price breaches

certain levels.

ACTION

Buy a Put with strike price A and a Call with strike price B (see Long Strangle graph).

Choose the strike prices according to which levels you believe will trigger large moves inthe spot.

Long Strangle


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EXAMPLE

You believe USD/INR will have a large swing in price if certain levels are breached. The

spot is 47.1730. You buy a one-month USD/INR Call with a strike of 47.19 for a premium

of 67 pips and a USD/INR Put with a strike of 47.16 for a premium of 67 pips.

UPSIDE

This strategy yields a profit if the spot is below 47.1466 or above 47.2034 at the time ofexpiry.

DOWNSIDE

The risk is limited to the cost of the premiums (134 pips), which will be lost if the options

are worthless at the time of expiry.

Example Long Strangle


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SCENARIO

You expect a moderate increase in the spot.

ACTION

Buy a Call with strike price A and sell a Call with strike price B (see Call Spread graph).

Strike price A would be selected roughly at-the-money. Strike price B should be placed at

the the value you expect the spot to have at the time the option matures.

Call Spread


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EXAMPLE

USD/INR spot is 47.1730. You expect it to increase to app. 47.20 within a month's time.

You buy a USD/INR Call with a strike of 47.18 for a premium of 105 pips. You sell a

USD/INR Call with a strike of 47.20 for a premium of 39 pips.

UPSIDE

You profit potential is any price above 47.1866, but with a ceiling of 47.20.

DOWNSIDE

The loss of the net premium paid, or 66 pips (the net value of the premium paid minus

the premium received), if the option is worthless at the time of expiry.

Example Call Spread


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The Delta measure describes how the value of an option changes as a result of

small changes in the underlying asset, assuming that all the other factors

influencing option pricing are constant.

The delta of an option can also be viewed as the required hedge for the option

against changes in the underlying spot, i.e. the position in the spot which ensuresthat the Profit/Loss on the option is offset by the Profit/Loss on the spot position.

Delta can also be viewed as the probability that the option will end in the money

If an investor buys a 40 Delta EUR/USD Call for one million, he/she can hedge this position by selling400,000 in the underlying asset - i.e. the spot. Alternatively, if the investor had bought a 30 Delta

EUR/USD Call he/she would have to sell 300,000 in the spot market to become delta neutral.

Delta


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The gamma measure describes how the delta of the option changes when the

underlying asset changes. Hence, the gamma also describes how the you should

change your hedge to remain delta neutral when the spot moves. All purchased

standard options, calls and puts, have positive gamma.

The gamma position also provides insight into the investor's view on the volatilityof the underlying asset, as a long position shows expectations of a volatile market

while a short position indicates that he/she expects a calm market

Gamma


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Theta shows how much value the option price will lose for everyday that passes

An option contract has a finite life, defined by the expiration date. As the option

approaches its maturity date, an option contract's expected value becomes more

certain with each day

This Time Value, also called Extrinsic Value, represents the uncertainty of an option

Theta is the calculation that shows how much of this time value is eroding as each

trading day passes - assuming all other inputs remain unchanged. Because of this

negative impact on an option price, the Theta will always be a negative number

For example, say an option has a theoretical price of 3.50 and is showing a Theta

value of -0.20. Tomorrow, if the underlying market opens unchanged (opens at the

same price as the previous days close) then the theoretical value of the option will

now be worth 3.30 (3.50 - 0.20)

Theta


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Rho is the change in option value that results from movements in interest rates

The value is represented as the change in theoretical price of the option for a 1

percentage point movement in the underlying interest rate

For example, say you're pricing a call option with a theoretical value of 2.50 that is

showing a Rho value of .25. If interest rates increase from 5% to 6%, then the price

of the call option, theoretically at least will increase from 2.50 to 2.75

Unlike the other option greeks, Rho is larger for options that are in the money and

decreases steadily as the option moves out of the money

Option Rho also increases with a greater amount of time to expiration

Rho


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Greek Long Short

Gamma Long Options position Short Options position

Delta Bought Call/Sold Put Sold Call/Bought Put

What the Greeks mean to me

Long In... Profit Loss

Delta Increase in Spot Decrease in Spot

Gamma High Real Volatility Low Real Volatility

Short In... Profit Loss

Delta Decrease in Spot Increase in Spot

Gamma Low Real Volatility High Real Volatility

The Greeks and my position

The Greeks and my profit and loss

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Derivatives Options

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