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Options
Stock markets by their very nature are fickle.
While fortunes can be made in a jiffy more often than not the scenario
is the reverse. Investing in stocks has two sides to it –a) Unlimited
profit potential from any upside (remember Infosys, HFCL etc) or b) a
downside which could make you a pauper.
Derivative products are
structured precisely for this reason -- to curtail the risk exposure
of an investor. Index futures and stock options are instruments that
enable you to hedge your portfolio or open positions in the market.
Option contracts allow you to run your profits while restricting your
downside risk.
Apart from risk
containment, options can be used for speculation and investors can
create a wide range of potential profit scenarios.
We have seen in the
Derivatives School how index futures can be used to protect oneself
from volatility or market risk. Here we will try and understand some
basic concepts of options.
What are options?
Some people remain
puzzled by options. The truth is that most people have been using
options for some time, because options are built into everything from
mortgages to insurance.
An option is a
contract, which gives the buyer the right, but not the obligation to
buy or sell shares of the underlying security at a specific price on
or before a specific date.
‘Option’, as the word
suggests, is a choice given to the investor to either honour the
contract; or if he chooses not to walk away from the contract.
To begin, there are two kinds of
options: Call Options and Put Options.
A Call Option is an
option to buy a stock at a specific price on or before a certain date.
In this way, Call options are like security deposits. If, for example,
you wanted to rent a certain property, and left a security deposit for
it, the money would be used to insure that you could, in fact, rent
that property at the price agreed upon when you returned. If you never
returned, you would give up your security deposit, but you would have
no other liability. Call options usually increase in value as the
value of the underlying instrument rises.
When you buy a Call
option, the price you pay for it, called the option premium, secures
your right to buy that certain stock at a specified price called the
strike price. If you decide not to use the option to buy the stock,
and you are not obligated to, your only cost is the option premium.
Put Options are options
to sell a stock at a specific price on or before a certain date. In
this way, Put options are like insurance policies
If you buy a new car,
and then buy auto insurance on the car, you pay a premium and are,
hence, protected if the asset is damaged in an accident. If this
happens, you can use your policy to regain the insured value of the
car. In this way, the put option gains in value as the value of the
underlying instrument decreases. If all goes well and the insurance is
not needed, the insurance company keeps your premium in return for
taking on the risk.
With a Put Option, you
can "insure" a stock by fixing a selling price. If something happens
which causes the stock price to fall, and thus, "damages" your asset,
you can exercise your option and sell it at its "insured" price level.
If the price of your stock goes up, and there is no "damage," then you
do not need to use the insurance, and, once again, your only cost is
the premium. This is the primary function of listed options, to allow
investors ways to manage risk.
Technically, an option
is a contract between two parties. The buyer receives a privilege for
which he pays a premium. The seller accepts an obligation for which he
receives a fee.
We will dwelve further into the
mechanics of call/put options in subsequent lessons.
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Call option
An option is a contract between two parties
giving the taker (buyer) the right, but not the obligation, to buy
or sell a parcel of shares at a predetermined price possibly on,
or before a predetermined date. To acquire this right the taker
pays a premium to the writer (seller) of the contract.
There are two types of options:
Call options
Call options give
the taker the right, but not the obligation, to buy the underlying
shares at a predetermined price, on or before a predetermined
date.
Illustration 1:
Raj purchases 1 Satyam Computer (SATCOM)
AUG 150 Call --Premium 8
This contract
allows Raj to buy 100 shares of SATCOM at Rs 150 per share at any
time between the current date and the end of next August. For this
privilege, Raj pays a fee of Rs 800 (Rs eight a share for 100
shares).
The buyer of a call
has purchased the right to buy and for that he pays a premium.
Now let us see how
one can profit from buying an option.
Sam purchases a
December call option at Rs 40 for a premium of Rs 15. That is he
has purchased the right to buy that share for Rs 40 in December.
If the stock rises above Rs 55 (40+15) he will break even and he
will start making a profit. Suppose the stock does not rise and
instead falls he will choose not to exercise the option and forego
the premium of Rs 15 and thus limiting his loss to Rs 15.

Let us take another
example of a call option on the Nifty to understand the concept
better.
Nifty is at 1310.
The following are Nifty options traded at following quotes.
|
Option
contract |
Strike price |
Call premium |
|
Dec Nifty |
1325 |
Rs 6,000 |
|
1345 |
Rs 2,000 |
|
|
|
|
Jan Nifty |
1325 |
Rs 4,500 |
|
1345 |
Rs 5000 |
A trader is of the
view that the index will go up to 1400 in Jan 2002 but does not
want to take the risk of prices going down. Therefore, he buys 10
options of Jan contracts at 1345. He pays a premium for buying
calls (the right to buy the contract) for 500*10= Rs 5,000/-.
In Jan 2002 the
Nifty index goes up to 1365. He sells the options or exercises the
option and takes the difference in spot index price which is
(1365-1345) * 200 (market lot) = 4000 per contract. Total profit =
40,000/- (4,000*10).
He had paid Rs 5,000/- premium for
buying the call option. So he earns by buying call option is Rs
35,000/- (40,000-5000).
If the index falls
below 1345 the trader will not exercise his right and will opt to
forego his premium of Rs 5,000. So, in the event the index falls
further his loss is limited to the premium he paid upfront, but
the profit potential is unlimited.
Call Options-Long & Short
Positions
When you expect prices to rise,
then you take a long position by buying calls. You are bullish.
When you expect prices to fall,
then you take a short position by selling calls. You are
bearish.
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Put Options
A
Put Option gives the holder of
the right to sell a specific number of shares of an agreed
security at a fixed price for a period of time.
eg: Sam purchases
1 INFTEC (Infosys Technologies) AUG 3500 Put --Premium 200
This contract
allows Sam to sell 100 shares INFTEC at Rs 3500 per share at any
time between the current date and the end of August. To have this
privilege, Sam pays a premium of Rs 20,000 (Rs 200 a share for 100
shares).
The buyer of a put
has purchased a right to sell. The owner of a put option has the
right to sell.
Illustration 2:
Raj is of the view that the a stock is
overpriced and will fall in future, but he does not want to take
the risk in the event of price rising so purchases a put option at
Rs 70 on ‘X’. By purchasing the put option Raj has the right to
sell the stock at Rs 70 but he has to pay a fee of Rs 15
(premium).
So he will
breakeven only after the stock falls below Rs 55 (70-15) and will
start making profit if the stock falls below Rs 55.

Illustration 3:
An investor on Dec
15 is of the view that Wipro is overpriced and will fall in future
but does not want to take the risk in the event the prices rise.
So he purchases a Put option on Wipro.
Quotes are as under:
Spot Rs 1040
Jan Put at 1050 Rs 10
Jan Put at 1070 Rs 30
He purchases 1000 Wipro Put at
strike price 1070 at Put price of Rs 30/-. He pays Rs 30,000/- as
Put premium.
His position in following price
position is discussed below.
- Jan Spot price of Wipro = 1020
- Jan Spot price of Wipro = 1080
In the first
situation the investor is having the right to sell 1000 Wipro
shares at Rs 1,070/- the price of which is Rs 1020/-. By
exercising the option he earns Rs (1070-1020) = Rs 50 per Put,
which totals Rs 50,000/-. His net income is Rs (50000-30000) = Rs
20,000.
In the second price
situation, the price is more in the spot market, so the investor
will not sell at a lower price by exercising the Put. He will have
to allow the Put option to expire unexercised. He looses the
premium paid Rs 30,000.
Put Options-Long & Short Positions
When you expect prices to fall,
then you take a long position by buying Puts. You are bearish.
When you expect prices to rise,
then you take a short position by selling Puts. You are bullish.
| |
CALL OPTIONS |
PUT OPTIONS |
| If
you expect a fall in price(Bearish) |
Short |
Long |
| If
you expect a rise in price (Bullish) |
Long |
Short |
SUMMARY:
|
CALL OPTION BUYER |
CALL OPTION WRITER (Seller) |
- Pays premium
- Right to exercise and buy
the shares
- Profits from rising prices
- Limited losses, Potentially
unlimited gain
|
- Receives premium
- Obligation to sell shares if
exercised
- Profits from falling prices
or remaining neutral
- Potentially unlimited
losses, limited gain
|
|
PUT OPTION BUYER |
PUT OPTION WRITER (Seller) |
- Pays premium
- Right to exercise and sell
shares
- Profits from falling prices
- Limited losses, Potentially
unlimited gain
|
- Receives premium
- Obligation to buy shares if
exercised
- Profits from rising prices
or remaining neutral
- Potentially unlimited
losses, limited gain
|
|
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Option styles
Settlement of
options is based on the expiry date. However, there are three
basic styles of options you will encounter which affect
settlement. The styles have geographical names, which have nothing
to do with the location where a contract is agreed! The styles
are:
European:
These options give the holder the right, but not the obligation,
to buy or sell the underlying instrument only on the expiry
date. This means that the option cannot be exercised early.
Settlement is based on a particular strike price at expiration.
Currently, in India only index options are European in nature.
eg:
Sam purchases 1 NIFTY AUG 1110 Call --Premium 20. The exchange
will settle the contract on the last Thursday of August. Since
there are no shares for the underlying, the contract is cash
settled.
American:
These options give the holder the right, but not the obligation,
to buy or sell the underlying instrument on or before the
expiry date. This means that the option can be exercised early.
Settlement is based on a particular strike price at expiration.
Options in stocks
that have been recently launched in the Indian market are
"American Options".
eg: Sam purchases
1 ACC SEP 145 Call --Premium 12
Here Sam can close
the contract any time from the current date till the expiration
date, which is the last Thursday of September.
American style
options tend to be more expensive than European style because they
offer greater flexibility to the buyer.
Option
Class & Series
Generally, for each underlying,
there are a number of options available: For this reason, we have
the terms "class" and "series".
An option "class"
refers to all options of the same type (call or put) and style
(American or European) that also have the same underlying.
eg: All Nifty call
options are referred to as one class.
An option series
refers to all options that are identical: they are the same type,
have the same underlying, the same expiration date and the same
exercise price.
|
Calls |
Puts |
|
. |
JUL |
AUG |
SEP |
JUL |
AUG |
SEP |
|
Wipro |
|
| 1300
|
45 |
60 |
75 |
15 |
20 |
28 |
| 1400
|
35 |
45 |
65 |
25 |
28
|
35
|
| 1500 |
20
|
42 |
48 |
30 |
40 |
55 |
eg: Wipro JUL 1300 refers to one series and trades take place at different
premiums
All calls are of
the same option type. Similarly, all puts are of the same option
type. Options of the same type that are also in the same class are
said to be of the same class. Options of the same class and with
the same exercise price and the same expiration date are said to
be of the same series |
Concepts
Important Terms
(Strike price,
In-the-money, Out-of-the-Money, At-the-Money, Covered call and Covered
Put)
Strike price: The Strike
Price denotes the price at which the buyer of the option has a right
to purchase or sell the underlying. Five different strike prices will
be available at any point of time. The strike price interval will be
of 20. If the index is currently at 1,410, the strike prices available
will be 1,370, 1,390, 1,410, 1,430, 1,450. The strike price is also
called Exercise Price. This price is fixed by the exchange for
the entire duration of the option depending on the movement of the
underlying stock or index in the cash market.
In-the-money:
A Call Option is said to be
"In-the-Money" if the strike price is less than the market price
of the underlying stock. A Put Option is In-The-Money when the strike
price is greater than the market price.
eg: Raj purchases 1
SATCOM AUG 190 Call --Premium 10
In the above example,
the option is "in-the-money", till the market price of SATCOM is
ruling above the strike price of Rs 190, which is the price at which
Raj would like to buy 100 shares anytime before the end of August.
Similary, if Raj had
purchased a Put at the same strike price, the option would have been
"in-the- money", if the market price of SATCOM was lower than Rs 190
per share.
Out-of-the-Money:
A Call Option is said to be
"Out-of-the-Money" if the strike price is greater than the market
price of the stock. A Put option is Out-Of-Money if the strike price
is less than the market price.
eg: Sam purchases 1
INFTEC AUG 3500 Call --Premium 150
In the above example,
the option is "out-of- the- money", if the market price of INFTEC is
ruling below the strike price of Rs 3500, which is the price at which
SAM would like to buy 100 shares anytime before the end of August.
Similary, if Sam had
purchased a Put at the same strike price, the option would have been
"out-of-the-money", if the market price of INFTEC was above Rs 3500
per share.
At-the-Money: The option with strike price equal to
that of the market price of the stock is considered as being
"At-the-Money" or Near-the-Money.
eg: Raj purchases 1
ACC AUG 150 Call or Put--Premium 10
In the above case, if
the market price of ACC is ruling at Rs 150, which is equal to the
strike price, then the option is said to be "at-the-money".
If the index is
currently at 1,410, the strike prices available will be 1,370, 1,390,
1,410, 1,430, 1,450. The strike prices for a call option that are
greater than the underlying (Nifty or Sensex) are said to be
out-of-the-money in this case 1430 and 1450 considering that the
underlying is at 1410. Similarly in-the-money strike prices will be
1,370 and 1,390, which are lower than the underlying of 1,410.
At these prices one can
take either a positive or negative view on the markets i.e. both call
and put options will be available. Therefore, for a single series 10
options (5 calls and 5 puts) will be available and considering that
there are three series a total number of 30 options will be available
to take positions in.
Covered Call
Option
Covered option helps
the writer to minimize his loss. In a covered call option, the
writer of the call option takes a corresponding long position in the
stock in the cash market; this will cover his loss in his option
position if there is a sharp increase in price of the stock. Further,
he is able to bring down his average cost of acquisition in the cash
market (which will be the cost of acquisition less the option premium
collected).
eg:
Raj believes that HLL has hit rock bottom at the level of Rs.182 and
it will move in a narrow range. He can take a long position in HLL
shares and at the same time write a call option with a strike price of
185 and collect a premium of Rs.5 per share. This will bring down the
effective cost of HLL shares to 177 (182-5). If the price stays below
185 till expiry, the call option will not be exercised and the writer
will keep the Rs.5 he collected as premium. If the price goes above
185 and the Option is exercised, the writer can deliver the shares
acquired in the cash market.
Covered Put
Option
Similarly, a writer of
a Put Option can create a covered position by selling the underlying
security (if it is already owned). The effective selling price will
increase by the premium amount (if the option is not exercised at
maturity). Here again, the investor is not in a position to take
advantage of any sharp increase in the price of the asset as the
underlying asset has already been sold. If there is a sharp decline in
the price of the underlying asset, the option will be exercised and
the investor will be left only with the premium amount. The loss in
the option exercised will be equal to the gain in the short position
of the asset.
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Pricing of
options
Options are used as
risk management tools and the valuation or pricing of the
instruments is a careful balance of market factors.
There are four major factors
affecting the Option premium:
- Price of Underlying
- Time to Expiry
- Exercise Price Time to Maturity
- Volatility of the Underlying
And two less important factors:
- Short-Term Interest Rates
- Dividends
Review of
Options Pricing Factors
The
Intrinsic Value of an Option
The intrinsic value
of an option is defined as the amount by which an option is
in-the-money, or the immediate exercise value of the option when
the underlying position is marked-to-market.
For a call option: Intrinsic Value
= Spot Price - Strike Price
For a put option: Intrinsic Value =
Strike Price - Spot Price
The intrinsic value
of an option must be positive or zero. It cannot be negative. For
a call option, the strike price must be less than the price of the
underlying asset for the call to have an intrinsic value greater
than 0. For a put option, the strike price must be greater than
the underlying asset price for it to have intrinsic value.
Price of underlying
The premium is affected by the
price movements in the underlying
instrument. For Call options – the
right to buy the underlying at a fixed strike
price – as the
underlying price rises so does its premium. As the underlying
price falls so does the cost of the option premium. For Put
options – the right to sell the underlying at a fixed strike
price – as the
underlying price rises, the premium falls; as the underlying price
falls the premium cost rises.
The following chart
summarises the above for Calls and Puts.
The Time Value of
an Option
Generally, the
longer the time remaining until an option’s expiration, the higher
its premium will be. This is because the longer an option’s
lifetime, greater is the possibility that the underlying share
price might move so as to make the option in-the-money. All other
factors affecting an option’s price remaining the same, the time
value portion of an option’s premium will decrease (or decay) with
the passage of time.
Note: This time
decay increases rapidly in the last several weeks of an option’s
life. When an option expires in-the-money, it is generally worth
only its intrinsic value.
Volatility
Volatility is the
tendency of the underlying security’s market price to fluctuate
either up or down. It reflects a price change’s magnitude; it does
not imply a bias toward price movement in one direction or the
other. Thus, it is a major factor in determining an option’s
premium. The higher the volatility of the underlying stock, the
higher the premium because there is a greater possibility that the
option will move in-the-money. Generally, as the volatility of an
under-lying stock increases, the premiums of both calls and puts
overlying that stock increase, and vice versa.
Higher
volatility=Higher premium
Lower
volatility = Lower premium
Interest rates
In general interest
rates have the least influence on options and equate approximately
to the cost of carry of a futures contract. If the size of the
options contract is very large, then this factor may take on
some importance.
All other factors being equal as interest rates rise, premium
costs fall and vice versa. The relationship can be thought of as
an opportunity cost. In order to buy an option, the buyer
must either borrow funds or use funds on deposit. Either way the
buyer incurs an interest rate cost. If interest rates are rising,
then the opportunity cost of buying options increases and to
compensate the buyer premium costs fall. Why should the buyer be
compensated? Because the option writer receiving the premium can
place the funds on deposit and receive more interest than was
previously anticipated. The situation is reversed when interest
rates fall – premiums rise. This time it is the writer who needs
to be compensated.
How do we measure
the impact of change in each of these pricing determinants on
option premium we shall learn in the next module. |
| Greeks
The options premium is determined by the
three factors mentioned earlier – intrinsic value, time value
and volatility. But there are more sophisticated tools used to
measure the potential variations of options premiums. They are
as follows:
Delta
Delta is the measure of an option’s
sensitivity to changes in the price of the underlying asset.
Therefore, its is the degree to which an option price will
move given a change in the underlying stock or index price,
all else being equal.
Change
in option premium Delta =
-------------------------------- Change
in underlying price
For example, an option with a delta of
0.5 will move Rs 5 for every change of Rs 10 in the underlying
stock or index.
Illustration:
A trader is considering buying a Call
option on a futures contract, which has a price of Rs 19. The
premium for the Call option with a strike price of Rs 19 is
0.80. The delta for this option is +0.5. This means that if
the price of the underlying futures contract rises to Rs 20 –
a rise of Re 1 – then the premium will increase by 0.5 x 1.00
= 0.50. The new option premium will be 0.80 + 0.50 = Rs
1.30.
Far out-of-the-money calls will have a
delta very close to zero, as the change in underlying price is
not likely to make them valuable or cheap. An at-the-money
call would have a delta of 0.5 and a deeply in-the-money call
would have a delta close to 1.
While Call deltas are positive, Put
deltas are negative, reflecting the fact that the put option
price and the underlying stock price are inversely related.
This is because if you buy a put your view is bearish and
expect the stock price to go down. However, if the stock price
moves up it is contrary to your view therefore, the value of
the option decreases. The put delta equals the call delta
minus 1.
It may be noted that if delta of your
position is positive, you desire the underlying asset to rise
in price. On the contrary, if delta is negative, you want the
underlying asset’s price to fall.
Uses: The knowledge of delta
is of vital importance for option traders because this
parameter is heavily used in margining and risk management
strategies. The delta is often called the hedge ratio. e.g. if you have a
portfolio of ‘n’ shares of a stock then ‘n’ divided by the
delta gives you the number of calls you would need to be short
(i.e. need to write) to create a riskless hedge – i.e. a
portfolio which would be worth the same whether the stock
price rose by a very small amount or fell by a very small
amount.
In such a "delta neutral" portfolio any
gain in the value of the shares held due to a rise in the
share price would be exactly offset by a loss on the value of
the calls written, and vice versa.
Note that as the delta changes with the
stock price and time to expiration the number of shares would
need to be continually adjusted to maintain the hedge. How
quickly the delta changes with the stock price is given by
gamma, which we shall learn
subsequently. |
| Gamma
This is the rate at which the delta value
of an option increases or decreases as a result of a move in
the price of the underlying instrument.
Change
in an option delta Gamma
=------------------------------------- Change
in underlying price
For example, if a Call option has a delta
of 0.50 and a gamma of 0.05, then a rise of ±1 in the
underlying means the delta will move to 0.55 for a price rise
and 0.45 for a price fall. Gamma is rather like the rate of
change in the speed of a car – its acceleration – in moving
from a standstill, up to its cruising speed, and braking back
to a standstill. Gamma is greatest for an ATM (at-the-money)
option (cruising) and falls to zero as an option moves deeply
ITM (in-the-money ) and OTM (out-of-the-money) (standstill).
If you are hedging a portfolio using the
delta-hedge technique described under "Delta", then you will
want to keep gamma as small as possible as the smaller it is
the less often you will have to adjust the hedge to maintain a
delta neutral position. If gamma is too large a small change
in stock price could wreck your hedge. Adjusting gamma,
however, can be tricky and is generally done using options --
unlike delta, it can't be done by buying or selling the
underlying asset as the gamma of the underlying asset is, by
definition, always zero so more or less of it won't affect the
gamma of the total portfolio.
|
Theta
It is a measure of an option’s sensitivity to
time decay. Theta is the change in option price given a one-day
decrease in time to expiration. It is a measure of time decay (or
time shrunk). Theta is generally used to gain an idea of how time
decay is affecting your portfolio.
Change
in an option premium Theta =
-------------------------------------- Change
in time to expiry
Theta is usually negative for an option as with
a decrease in time, the option value decreases. This is due to the
fact that the uncertainty element in the price decreases.
Assume an option has a premium of 3 and a theta
of 0.06. After one day it will decline to 2.94, the second day to
2.88 and so on. Naturally other factors, such as changes in value of
the underlying stock will alter the premium. Theta is only concerned
with the time value. Unfortunately, we cannot predict with accuracy
the change’s in stock market’s value, but we can measure exactly the
time remaining until expiration.
| Vega
This is a measure of the sensitivity of
an option price to changes in market volatility. It is the
change of an option premium for a given change – typically 1%
– in the underlying volatility.
Change
in an option premium Vega =
----------------------------------------- Change
in volatility
If for example, XYZ stock has a
volatility factor of 30% and the current premium is 3, a vega
of .08 would indicate that the premium would increase to 3.08
if the volatility factor increased by 1% to 31%. As the stock
becomes more volatile the changes in premium will increase in
the same proportion. Vega measures the sensitivity of the
premium to these changes in volatility.
What practical use is the vega to a
trader? If a trader maintains a delta neutral position, then
it is possible to trade options purely in terms of volatility
– the trader is not exposed to changes in underlying prices.
|
| Rho
The change in option price given a one
percentage point change in the risk-free interest rate. Rho
measures the change in an option’s price per unit increase
–typically 1% – in the cost of funding the
underlying.
Change
in an option premium Rho =
--------------------------------------------------- Change
in cost of funding underlying
Example:
Assume the value of Rho is 14.10. If the
risk free interest rates go up by 1% the price of the option
will move by Rs 0.14109. To put this in another way: if the
risk-free interest rate changes by a small amount, then the
option value should change by 14.10 times that amount. For
example, if the risk-free interest rate increased by 0.01
(from 10% to 11%), the option value would change by 14.10*0.01
= 0.14. For a put option the relationship is inverse. If the
interest rate goes up the option value decreases and
therefore, Rho for a put option is negative. In general Rho
tends to be small except for long-dated options.
|
Options
Pricing Models
There are various option pricing models
which traders use to arrive at the right value of the option. Some
of the most popular models have been enumerated below.
The Binomial Pricing Model
The binomial model is an options pricing model
which was developed by William Sharpe in 1978. Today, one finds a
large variety of pricing models which differ according to their
hypotheses or the underlying instruments upon which they are based
(stock options, currency options, options on interest rates).
The Black & Scholes
Model
The Black & Scholes model was published in
1973 by Fisher Black and Myron Scholes. It is one of the most
popular options pricing models. It is noted for its relative
simplicity and its fast mode of calculation: unlike the binomial
model, it does not rely on calculation by iteration.
The intention of this section is to introduce
you to the basic premises upon which this pricing model rests. A
complete coverage of this topic is material for an advanced
course
The Black-Scholes model is used to calculate a
theoretical call price (ignoring dividends paid during the life of
the option) using the five key determinants of an option's price:
stock price, strike price, volatility, time to expiration, and
short-term (risk free) interest rate.
The original formula for calculating the
theoretical option price (OP) is as follows:
Where:

The variables are:
S = stock price X =
strike price t = time remaining until
expiration, expressed as a percent of a year r = current continuously compounded risk-free
interest rate v = annual volatility of stock
price (the standard deviation of the short-term returns over one
year). ln = natural logarithm N(x) = standard normal cumulative distribution
function e = the exponential
function
Lognormal
distribution: The model is based on a lognormal distribution
of stock prices, as opposed to a normal, or bell-shaped,
distribution. The lognormal distribution allows for a stock price
distribution of between zero and infinity (ie no negative prices)
and has an upward bias (representing the fact that a stock price can
only drop 100 per cent but can rise by more than 100 per cent).
Risk-neutral
valuation: The expected rate of return of the stock (ie
the expected rate of growth of the underlying asset which equals the
risk free rate plus a risk premium) is not one of the variables in the
Black-Scholes model (or any other model for option valuation). The
important implication is that the price of an option is completely
independent of the expected growth of the underlying asset. Thus,
while any two investors may strongly disagree on the rate of return
they expect on a stock they will, given agreement to the assumptions
of volatility and the risk free rate, always agree on the fair price
of the option on that underlying asset.
The key concept underlying the valuation of all
derivatives -- the fact that price of an option is independent of
the risk preferences of investors -- is called risk-neutral valuation. It means that all
derivatives can be valued by assuming that the return from their
underlying assets is the risk free rate.
Limitation: Dividends are ignored in the basic
Black-Scholes formula, but there are a number of widely used
adaptations to the original formula, which I use in my models, which
enable it to handle both discrete and continuous dividends
accurately.
However, despite these adaptations the
Black-Scholes model has one major limitation: it cannot be used to
accurately price options with an American-style exercise as it only
calculates the option price at one point in time -- at expiration.
It does not consider the steps along the way where there could be
the possibility of early exercise of an American option.
As all exchange traded equity options have
American-style exercise (ie they can be exercised at any time as
opposed to European options which can only be exercised at
expiration) this is a significant limitation.
The exception to this is an American call on a
non-dividend paying asset. In this case the call is always worth the
same as its European equivalent as there is never any advantage in
exercising early.
Advantage: The main advantage of the
Black-Scholes model is speed -- it lets you calculate a very large
number of option prices in a very short time. Since, high accuracy
is not critical for American option pricing (eg when animating a
chart to show the effects of time decay) using Black-Scholes is a
good option. But, the option of using the binomial model is also
advisable for the relatively few pricing and profitability numbers
where accuracy may be important and speed is irrelevant. You can
experiment with the Black-Scholes model using on-line options
pricing calculator.
The Binomial Model
The binomial model breaks down the time to
expiration into potentially a very large number of time intervals,
or steps. A tree of stock prices is initially produced working
forward from the present to expiration. At each step it is assumed
that the stock price will move up or down by an amount calculated
using volatility and time to expiration. This produces a binomial
distribution, or recombining tree, of underlying stock prices. The
tree represents all the possible paths that the stock price could
take during the life of the option.
At the end of the tree -- ie at expiration of
the option -- all the terminal option prices for each of the final
possible stock prices are known as they simply equal their intrinsic
values.
Next the option prices at each step of the tree
are calculated working back from expiration to the present. The
option prices at each step are used to derive the option prices at
the next step of the tree using risk neutral valuation based on the
probabilities of the stock prices moving up or down, the risk free
rate and the time interval of each step. Any adjustments to stock
prices (at an ex-dividend date) or option prices (as a result of
early exercise of American options) are worked into the calculations
at the required point in time. At the top of the tree you are left
with one option price.
Advantage: The big advantage the
binomial model has over the Black-Scholes model is that it can be
used to accurately price American options. This is because, with the
binomial model it's possible to check at every point in an option's
life (ie at every step of the binomial tree) for the possibility of
early exercise (eg where, due to eg a dividend, or a put being
deeply in the money the option price at that point is less than the
its intrinsic value).
Where an early exercise point is found it is
assumed that the option holder would elect to exercise and the
option price can be adjusted to equal the intrinsic value at that
point. This then flows into the calculations higher up the tree and
so on.
Limitation: As mentioned before the main disadvantage of
the binomial model is its relatively slow speed. It's great for half
a dozen calculations at a time but even with today's fastest PCs
it's not a practical solution for the calculation of thousands of
prices in a few seconds which is what's required for the production
of the animated charts in my strategy evaluation model
 
Bull Market
Strategies
Calls in a Bullish Strategy
An investor with a bullish market outlook
should buy call options. If you expect the market price of the
underlying asset to rise, then you would rather have the right
to purchase at a specified price and sell later at a higher
price than have the obligation to deliver later at a higher
price.


The investor's profit potential buying a
call option is unlimited. The investor's profit is the the
market price less the exercise price less the premium. The
greater the increase in price of the underlying, the greater
the investor's profit.
The investor's potential loss is limited.
Even if the market takes a drastic decline in price levels,
the holder of a call is under no obligation to exercise the
option. He may let the option expire worthless.
The investor breaks even when the market
price equals the exercise price plus the premium.
An increase in volatility will increase
the value of your call and increase your return. Because of
the increased likelihood that the option will become in-
the-money, an increase in the underlying volatility (before
expiration), will increase the value of a long options
position. As an option holder, your return will also
increase.
A simple example will illustrate the
above:
Suppose there is a call option with a
strike price of Rs 2000 and the option premium is Rs 100. The
option will be exercised only if the value of the underlying
is greater than Rs 2000 (the strike price). If the buyer
exercises the call at Rs 2200 then his gain will be Rs 200.
However, this would not be his actual gain for that he will
have to deduct the Rs 200 (premium) he has paid.
The profit can be derived as follows
Profit = Market price - Exercise price -
Premium Profit = Market price – Strike
price – Premium.
2200 –
2000 – 100 = Rs 100
Top
Puts in a Bullish Strategy
An investor with a bullish market outlook
can also go short on a Put option. Basically, an investor
anticipating a bull market could write Put options. If the
market price increases and puts become out-of-the-money,
investors with long put positions will let their options
expire worthless.
By writing Puts, profit potential is
limited. A Put writer profits when the price of the underlying
asset increases and the option expires worthless. The maximum
profit is limited to the premium received.
However, the potential loss is unlimited.
Because a short put position holder has an obligation to
purchase if exercised. He will be exposed to potentially large
losses if the market moves against his position and
declines.
The break-even point occurs when the
market price equals the exercise price: minus the premium. At
any price less than the exercise price minus the premium, the
investor loses money on the transaction. At higher prices, his
option is profitable.
An increase in volatility will increase
the value of your put and decrease your return. As an option
writer, the higher price you will be forced to pay in order to
buy back the option at a later date , lower is the
return.
Top
Bullish Call Spread Strategies
A vertical call spread is the
simultaneous purchase and sale of identical call options but
with different exercise prices.
To "buy a call spread" is to purchase a
call with a lower exercise price and to write a call with a
higher exercise price. The trader pays a net premium for the
position.
To "sell a call spread" is the opposite,
here the trader buys a call with a higher exercise price and
writes a call with a lower exercise price, receiving a net
premium for the position.
An investor with a bullish market outlook
should buy a call spread. The "Bull Call Spread" allows the
investor to participate to a limited extent in a bull market,
while at the same time limiting risk exposure.


To put on a bull spread, the trader needs
to buy the lower strike call and sell the higher strike call.
The combination of these two options will result in a bought
spread. The cost of Putting on this position will be the
difference between the premium paid for the low strike call
and the premium received for the high strike call.
The investor's profit potential is
limited. When both calls are in-the-money, both will be
exercised and the maximum profit will be realised. The
investor delivers on his short call and receives a higher
price than he is paid for receiving delivery on his long
call.

The investors's potential loss is
limited. At the most, the investor can lose is the net
premium. He pays a higher premium for the lower exercise price
call than he receives for writing the higher exercise price
call.
The investor breaks even when the market
price equals the lower exercise price plus the net premium. At
the most, an investor can lose is the net premium paid. To
recover the premium, the market price must be as great as the
lower exercise price plus the net premium.
An example of a Bullish call spread:
Let's assume that the cash price of a
scrip is Rs 100 and you buy a November call option with a
strike price of Rs 90 and pay a premium of Rs 14. At the same
time you sell another November call option on a scrip with a
strike price of Rs 110 and receive a premium of Rs 4. Here you
are buying a lower strike price option and selling a higher
strike price option. This would result in a net outflow of Rs
10 at the time of establishing the spread.
Now let us look at the fundamental reason
for this position. Since this is a bullish strategy, the first
position established in the spread is the long lower strike
price call option with unlimited profit potential. At the same
time to reduce the cost of puchase of the long position a
short position at a higher call strike price is established.
While this not only reduces the outflow in terms of premium
but his profit potential as well as risk is limited. Based on
the above figures the maximum profit, maximum loss and
breakeven point of this spread would be as follows:
Maximum profit = Higher strike price -
Lower strike price - Net premium
paid
= 110 - 90 - 10 = 10
Maximum Loss = Lower strike premium -
Higher strike premium
= 14 - 4 = 10
Breakeven Price = Lower strike price +
Net premium paid
= 90 + 10 = 100
Top
Bullish Put Spread Strategies
A vertical Put spread is the simultaneous
purchase and sale of identical Put options but with different
exercise prices.
To "buy a put spread" is to purchase a
Put with a higher exercise price and to write a Put with a
lower exercise price. The trader pays a net premium for the
position.
To "sell a put spread" is the opposite:
the trader buys a Put with a lower exercise price and writes a
put with a higher exercise price, receiving a net premium for
the position.
An investor with a bullish market outlook
should sell a Put spread. The "vertical bull put spread"
allows the investor to participate to a limited extent in a
bull market, while at the same time limiting risk
exposure.


To put on a bull spread, a trader sells
the higher strike put and buys the lower strike put. The bull spread can be created by buying
the lower strike and selling the higher strike of either calls
or put. The difference between the premiums paid and received
makes up one leg of the spread.
The investor's profit potential is
limited. When the market price reaches or exceeds the higher
exercise price, both options will be out-of-the-money and will
expire worthless. The trader will realize his maximum profit,
the net premium

The investor's potential loss is also
limited. If the market falls, the options will be
in-the-money. The puts will offset one another, but at
different exercise prices.
The investor breaks-even when the market
price equals the lower exercise price less the net premium.
The investor achieves maximum profit i.e the premium received,
when the market price moves up beyond the higher exercise
price (both puts are then worthless).
An example of a bullish put
spread.
Lets us assume that the cash price of the
scrip is Rs 100. You now buy a November put option on a scrip
with a strike price of Rs 90 at a premium of Rs 5 and sell a
put option with a strike price of Rs 110 at a premium of Rs
15.
The first position is a short put at a
higher strike price. This has resulted in some inflow in terms
of premium. But here the trader is worried about risk and so
caps his risk by buying another put option at the lower strike
price. As such, a part of the premium received goes off and
the ultimate position has limited risk and limited profit
potential. Based on the above figures the maximum profit,
maximum loss and breakeven point of this spread would be as
follows:
Maximum profit = Net option premium
income or net credit
= 15 - 5 = 10
Maximum loss = Higher strike price -
Lower strike price - Net premium received
= 110 - 90 - 10 = 10
Breakeven Price = Higher Strike price -
Net premium income
= 110 - 10 = 100 |
Bear Market
Strategies
Puts in a Bearish Strategy
When you purchase a put you are long and
want the market to fall. A put option is a bearish position.
It will increase in value if the market falls. An investor
with a bearish market outlook shall buy put options. By
purchasing put options, the trader has the right to choose
whether to sell the underlying asset at the exercise price. In
a falling market, this choice is preferable to being obligated
to buy the underlying at a price higher.


An investor's profit potential is
practically unlimited. The higher the fall in price of the
underlying asset, higher the profits.
The investor's potential loss is limited.
If the price of the underlying asset rises instead of falling
as the investor has anticipated, he may let the option expire
worthless. At the most, he may lose the premium for the
option.
The trader's breakeven point is the
exercise price minus the premium. To profit, the market price
must be below the exercise price. Since the trader has paid a
premium he must recover the premium he paid for the option.
An increase in volatility will increase
the value of your put and increase your return. An increase in
volatility will make it more likely that the price of the
underlying instrument will move. This increases the value of
the option.
Top
Calls in a Bearish
Strategy
Another option for a bearish investor is
to go short on a call with the intent to purchase it back in
the future. By selling a call, you have a net short position
and needs to be bought back before expiration and cancel out
your position.
For this an investor needs to write a
call option. If the market price falls, long call holders will
let their out-of-the-money options expire worthless, because
they could purchase the underlying asset at the lower market
price.


The investor's profit potential is
limited because the trader's maximum profit is limited to the
premium received for writing the option.
Here the loss potential is unlimited
because a short call position holder has an obligation to sell
if exercised, he will be exposed to potentially large losses
if the market rises against his position.
The investor breaks even when the market
price equals the exercise price: plus the premium. At any
price greater than the exercise price plus the premium, the
trader is losing money. When the market price equals the
exercise price plus the premium, the trader breaks
even.
An increase in volatility will increase
the value of your call and decrease your return. When the option writer has to buy back
the option in order to cancel out his position, he will be
forced to pay a higher price due to the increased value of the
calls.
Top
Bearish Put Spread
Strategies
A vertical put spread is the simultaneous
purchase and sale of identical put options but with different
exercise prices.
To "buy a put spread" is to purchase a
put with a higher exercise price and to write a put with a
lower exercise price. The trader pays a net premium for the
position.
To "sell a put spread" is the opposite.
The trader buys a put with a lower exercise price and writes a
put with a higher exercise price, receiving a net premium for
the position.
To put on a bear put spread you buy the
higher strike put and sell the lower strike put. You sell the lower strike and buy the
higher strike of either calls or puts to set up a bear
spread.
An investor with a bearish market outlook should: buy a put
spread. The "Bear Put Spread" allows the investor to
participate to a limited extent in a bear market, while at the
same time limiting risk exposure.


The investor's profit potential is
limited. When the market price falls to or below the lower
exercise price, both options will be in-the-money and the
trader will realize his maximum profit when he recovers the
net premium paid for the options.
The investor's potential loss is limited.
The trader has offsetting positions at different exercise
prices. If the market rises rather than falls, the options
will be out-of-the-money and expire worthless. Since the
trader has paid a net premium
The investor breaks even when the market
price equals the higher exercise price less the net premium.
For the strategy to be profitable, the market price must fall.
When the market price falls to the high exercise price less
the net premium, the trader breaks even. When the market falls
beyond this point, the trader profits.
An example of a bearish put
spread.
Lets assume that the cash price of the
scrip is Rs 100. You buy a November put option on a scrip with
a strike price of Rs 110 at a premium of Rs 15 and sell a put
option with a strike price of Rs 90 at a premium of Rs 5.
In this bearish position the put is taken
as long on a higher strike price put with the outgo of some
premium. This position has huge profit potential on downside.
If the trader may recover a part of the premium paid by him by
writing a lower strike price put option. The resulting
position is a mildly bearish position with limited risk and
limited profit profile. Though the trader has reduced the cost
of taking a bearish position, he has also capped the profit
portential as well. The maximum profit, maximum loss and
breakeven point of this spread would be as follows:
Maximum profit = Higher strike price
option - Lower strike price option
- Net premium paid
= 110 - 90 - 10 = 10
Maximum loss = Net premium paid
= 15 - 5 = 10
Breakeven Price = Higher strike price -
Net premium paid
= 110 - 10 = 100
Top
Bearish Call Spread
Strategies
A vertical call spread is the simultaneous purchase and
sale of identical call options but with different exercise
prices.
To "buy a call spread" is to purchase a
call with a lower exercise price and to write a call with a
higher exercise price. The trader pays a net premium for the
position.
To "sell a call spread" is the opposite:
the trader buys a call with a higher exercise price and writes
a call with a lower exercise price, receiving a net premium
for the position.
To put on a bear call spread you sell the
lower strike call and buy the higher strike call. An investor
sells the lower strike and buys the higher strike of either
calls or puts to put on a bear spread.
An investor with a bearish market outlook
should: sell a call spread. The "Bear Call Spread" allows the
investor to participate to a limited extent in a bear market,
while at the same time limiting risk exposure.


The investor's profit potential is
limited. When the market price falls to the lower exercise
price, both out-of-the-money options will expire worthless.
The maximum profit that the trader can realize is the net
premium: The premium he receives for the call at the higher
exercise price.
Here the investor's potential loss is
limited. If the market rises, the options will offset one
another. At any price greater than the high exercise price,
the maximum loss will equal high exercise price minus low
exercise price minus net premium.
The investor breaks even when the market
price equals the lower exercise price plus the net premium.
The strategy becomes profitable as the market price declines.
Since the trader is receiving a net premium, the market price
does not have to fall as low as the lower exercise price to
breakeven.

An example of a bearish call
spread.
Let us assume that the cash price of the
scrip is Rs 100. You now buy a November call option on a scrip
with a strike price of Rs 110 at a premium of Rs 5 and sell a
call option with a strike price of Rs 90 at a premium of Rs
15.
In this spread you have to buy a higher
strike price call option and sell a lower strike price option.
As the low strike price option is more expensive than the
higher strike price option, it is a net credit startegy. The
final position is left with limited risk and limited profit.
The maximum profit, maximum loss and breakeven point of this
spread would be as follows:
Maximum profit = Net premium
received
= 15 - 5 = 10
Maximum loss = Higher strike price option
- Lower strike price option -
Net premium received
= 110 - 90 - 10 = 10
Breakeven Price = Lower strike price +
Net premium paid
= 90 + 10 = 100 |
Volatile Market
Strategies
Straddles in a Volatile Market
Outlook
Volatile market trading strategies are
appropriate when the trader believes the market will move but
does not have an opinion on the direction of movement of the
market. As long as there is significant movement upwards or
downwards, these strategies offer profit opportunities. A
trader need not be bullish or bearish. He must simply be of
the opinion that the market is volatile.
A trader, viewing a market as volatile,
should buy option straddles. A "straddle purchase" allows the
trader to profit from either a bull market or from a bear
market.


Here the investor's profit potential is
unlimited. If the market is volatile, the trader can profit
from an up- or downward movement by exercising the appropriate
option while letting the other option expire worthless. (Bull
market, exercise the call; bear market, the put.)
While the investor's potential loss is
limited. If the price of the underlying asset remains stable
instead of either rising or falling as the trader anticipated,
the most he will lose is the premium he paid for the
options.
In this case the trader has long two
positions and thus, two breakeven points. One is for the call,
which is exercise price plus the premiums paid, and the other
for the put, which is exercise price minus the premiums
paid.
Strangles in a Volatile Market
Outlook
A strangle is similar to a straddle,
except that the call and the put have different exercise
prices. Usually, both the call and the put are
out-of-the-money.
To "buy a strangle" is to purchase a call
and a put with the same expiration date, but different
exercise prices.
To "sell a strangle" is to write a call
and a put with the same expiration date, but different
exercise prices.
A trader, viewing a market as volatile,
should buy strangles. A "strangle purchase" allows the trader
to profit from either a bull or bear market. Because the
options are typically out-of-the-money, the market must move
to a greater degree than a straddle purchase to be
profitable.
The trader's profit potential is
unlimited. If the market is volatile, the trader can profit
from an up- or downward movement by exercising the appropriate
option, and letting the other expire worthless. (In a bull
market, exercise the call; in a bear market, the
put).
The investor's potential loss is limited.
Should the price of the underlying remain stable, the most the
trader would lose is the premium he paid for the options. Here
the loss potential is also very minimal because, the more the
options are out-of-the-money, the lesser the
premiums.
Here the trader has two long positions
and thus, two breakeven points. One for the call, which
breakevens when the market price equal the high exercise price
plus the premium paid, and for the put, when the market price
equals the low exercise price minus the premium paid. Pic:Opt35
The Short Butterfly Call
Spread
Like the volatility positions we have
looked at so far, the Short Butterfly position will realize a
profit if the market makes a substantial move. It also uses a
combination of puts and calls to achieve its profit/loss
profile - but combines them in such a manner that the maximum
profit is limited.
You are short the September 40-45-50
butterfly with the underlying at 45. You: you are neutral but
want the market to move in either direction. The position is a neutral one -
consisting of two short options balanced out with two long
ones.
Which of these positions is a short
butterfly spread? The graph on the left. The profit loss profile of a short
butterfly spread looks like two short options coming together
at the center Calls.

The spread shown above was constructed by
using 1 short call at a low exercise price, two long calls at
a medium exercise price and 1 short call at a high exercise
price.
Your potential gains or losses are:
limited on both the upside and the downside. Say you had build a short 40-45-50
butterfly. The position would yield a profit only if the
market moves below 40 or above 50. The maximum loss is also
limited.
The Call Ratio Backspread
The call ratio backspread is similar in
contruction to the short butterfly call spread you looked at
in the previous section. The only difference is that you omit
one of the components (or legs) used to build the short
butterfly when constructing a call ratio backspread.
When putting on a call ratio backspread,
you are neutral but want the market to move in either
direction. The call ratio backspread will lose money if the
market sits. The market outlook one would have in putting on
this position would be for a volatile market, with greater
probability that the market will rally.
To put on a call ratio backspread, you
sell one of the lower strike and buy two or more of the higher
strike. By selling an expensive lower strike option and buying
two less expensive high strike options, you receive an initial
credit for this position. The maximum loss is then equal to
the high strike price minus the low strike price minus the
initial net premium received.
Your potential gains are limited on the
downside and unlimited on the upside. The profit on the downside is limited to
the initial net premium received when setting up the spread.
The upside profit is unlimited.
An increase in implied volatility will
make your spread more profitable. Increased volatility
increases a long option position's value. The greater number
of long options will cause this spread to become more
profitable when volatility increases.
The Put Ratio Backspread
In combination positions (e.g. bull
spreads, butterflys, ratio spreads), one can use calls or puts
to achieve similar, if not identical, profit profiles. Like
its call counterpart, the put ratio backspread combines
options to create a spread which has limited loss potential
and a mixed profit potential.
It is created by combining long and short
puts in a ratio of 2:1 or 3:1. In a 3:1 spread, you would buy
three puts at a low exercise price and write one put at a high
exercise price. While you may, of course, extend this position
out to six long and two short or nine long and three short, it
is important that you respect the (in this case) 3:1 ratio in
order to maintain the put ratio backspread profit/loss
profile.
When you put on a put ratio backspread:
are neutral but want the market to move in either direction.
Your market expectations here would
be for a volatile market with a greater probability that the
market will fall than rally.
How would the profit/loss profile of a
put ratio backspread differ from a call ratio
backspread?
Unlimited profit would be realized on the
downside. The two long puts offset
the short put and result in practically unlimited profit on
the bearish side of the market. The cost of the long puts is
offset by the premium received for the (more expensive) short
put, resulting in a net premium received.
To put on a put ratio backspread, you:
buy two or more of the lower strike and sell one of the higher
strike. You sell the more expensive
put and buy two or more of the cheaper put. One usually
receives an initial net premium for putting on this spread.
The Maximum loss is equal to: High strike price - Low strike
price - Initial net premium received.
For eg if the ratio backspread is 45 days
before expiration. Considering only the bearish side of the
market, an increase in volatility increases profit/loss and
the passage of time decreases profit/loss.
The low breakeven point indicated on the
graph is equal to the lower of the two exercise prices...
minus the call premiums paid, minus the net premiums received.
The higher of this position's two breakeven points is simply
the high exercise price minus the net
premium. |
Stable Market
Strategies
Straddles in a Stable Market
Outlook
Volatile market trading strategies are
appropriate when the trader believes the market will move but
does not have an opinion on the direction of movement of the
market. As long as there is significant movement upwards or
downwards, these strategies offer profit opportunities. A
trader need not be bullish or bearish. He must simply be of
the opinion that the market is volatile. This market outlook
is also referred to as "neutral volatility."
A trader, viewing a market as stable,
should: write option straddles. A "straddle sale" allows the
trader to profit from writing calls and puts in a stable
market environment.


The investor's profit potential is
limited. If the market remains stable, traders long
out-of-the-money calls or puts will let their options expire
worthless. Writers of these options will not have be called to
deliver and will profit from the sum of the premiums
received.
The investor's potential loss is
unlimited. Should the price of the underlying rise or fall,
the writer of a call or put would have to deliver, exposing
himself to unlimited loss if he has to deliver on the call and
practically unlimited loss if on the put.
The breakeven points occur when the
market price at expiration equals the exercise price plus the premium and minus the premium.
The trader is short two positions and thus, two breakeven
points; One for the call (common exercise price plus the
premiums paid), and one for the put (common exercise price
minus the premiums paid).
Strangles in a Stable Market
Outlook
A strangle is similar to a straddle,
except that the call and the put have different exercise
prices. Usually, both the call and the put are
out-of-the-money.
To "buy a strangle" is to purchase a call
and a put with the same expiration date, but different
exercise prices. Usually the call strike price is higher than
the put strike price.
To "sell a strangle" is to write a call
and a put with the same expiration date, but different
exercise prices.
A trader, viewing a market as stable,
should: write strangles. A "strangle
sale" allows the trader to profit from a stable
market.
The investor's profit potential is:
unlimited. If the market remains
stable, investors having out-of-the-money long put or long
call positions will let their options expire
worthless.
The investor's potential loss is:
unlimited. If the price of the
underlying interest rises or falls instead of remaining stable
as the trader anticipated, he will have to deliver on the call
or the put.
The breakeven points occur when market
price at expiration equals...the high exercise price plus the
premium and the low exercise price minus the premium. The trader is short two positions and
thus, two breakeven points. One for the call (high exercise
price plus the premiums paid), and one for the put (low
exercise price minus the premiums paid).

Why would a trader choose to sell a
strangle rather than a straddle?
The risk is lower with a strangle.
Although the seller gives up a substantial amount of potential
profit by selling a strangle rather than a straddle, he also
holds less risk. Notice that the strangle requires more of a
price move in both directions before it begins to lose
money.
Long Butterfly Call
Spread Strategy The long butterfly call spread is a
combination of a bull spread and a bear spread, utilizing
calls and three different exercise prices.
A long butterfly call spread involves:
To put on the September 40-45-50 long
butterfly, you: buy the 40 and 50 strike and sell two 45
strikes. This spread is put on by
purchasing one each of the outside strikes and selling two of
the inside strike. To put on a short butterfly, you do just
the opposite.
The investor's profit potential is
limited. Maximum profit is attained
when the market price of the underlying interest equals the
mid-range exercise price (if the exercise prices are
symmetrical).

The investor's potential loss is:
limited. The maximum loss is limited
to the net premium paid and is realized when the market price
of the underlying asset is higher than the high exercise price
or lower than the low exercise price.
The breakeven points occur when the
market price at expiration equals ... the high exercise price
minus the premium and the low exercise price plus the premium.
The strategy is profitable when the market price is between
the low exercise price plus the net premium and the high
exercise price minus the net premium.

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