Derivatives Options
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Transcript of 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