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Exotic Options andTrading Strategies
Workbook and Reference
Guide
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SECTION 1 OPTIONSBASICS
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Options
1.1. Definition and Features
An options contract gives the holder the right, but not the obligation, to buy or sell a givenunderlying product at a fixed price on a given date in exchange for a premium.
The following is key terminology for options contracts:Term Meaning
Strike price Price at which the option buyer has the right to buy or sell theunderlying.
Expiration Date and time on which the holder/buyer of the option loses theright to buy or sell.
Writer The option seller is also known as the option writer
Premium The amount paid by the option buyer to the option writer for theright.
Call option Buyer has the right to buy the underlying
Put option Buyer has the right to sell the underlying
Exercise Process of deciding and advising option seller/writer of intentionto exercise the right under the option
Life of option As exercise period - time until expiration
Exercise period As life of option - time until expiration
American Option Can be exercised at any time in a given period
European Option Exercise on expiration date only
Bermudan Option Exercise on a given range of dates.
In the money Given current market rates it is likely that the option will beexercised. A call option is in the money when the strike price isbelow the current market price. A put option is in the moneywhen the strike price is above the current market price
Out of the money Given current market rates it is unlikely that the option will beexercised.
At the money When the strike price is equal to the current market price
Breakeven Price The price of the underlying at which neither a profit nor a loss ismade. This occurs where underlying price - premium=strike price
Naked options Where the writer of a call option does not hold the underlyingstock or the right to buy the underlying stock if the buyer of theoption exercises his right then he is said to be exposed, uncoveredor naked
Covered options Where the writer of a call option holds the underlying stock orholds a hedge to buy the underlying stock if the buyer exercisesagainst him he is said to be covered.
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Term Meaning
Assignment Act by which the exchange designates an option writer forfulfilment of his obligation to sell or buy the underlying assetunder an exchange traded contract.
At the Money, Out of the Money, In the Money
The most profitable time to exercise an option is when it is In the Money. The following tableshows how an option contract moves in and out of the money as the price of the underlyingmoves:
-4
-3
-2
-1
0
1
2
3
4
Underlying Price
ProfitorLoss
Profit or Loss 3 2 1 0 -1 -2 -3
16 17 18 19 20 21 22
In the Money
Out Of the Money
At the
mone
Options may be standardised Exchange Traded Contracts (XTC) or customised Over the Counter(OTC) contracts. Exchange traded contracts may be exposed to daily margin calls where theexchange takes a proportion of the value of the loss as a deposit from the buyer.Exchange members and brokers charge commission to their clients to conduct the trades on theirbehalf.Exchanges include:
LIFFE (London International Financial Futures and Options Exchange
CBOT: Chicago Board of Trade
CME: Chicago Mercantile Exchange. A more detailed list is included as an Appendix.
Exchange traded options usually have expiry out to 2 years. Over the counter options can be
written for any period but typically not more than 10 years.OTC options include caps, collars and floors, which are covered in a separate section.The risk for option writers can be limitless especially where naked options are sold. These occurwhere the writer does not hold the underlying and is therefore exposed to movements in themarket price.Underlying includes
Currencies
Interest rates such as 3 month libor
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Securities
Swaps (see separate section on swaptions)
Futures
In the financial times on Weds 23rd October the following prices were quoted for three-month
Eurodollar options on CME. As per the contract specifications detailed below this gives thebuyer the right to buy one Eurodollar futures contract on CME.
Strike Price Calls Puts
Nov Dec Jan Nov Dec Jan
98.125 0.13 0.06 - 0.03 0.05 -
98.25 0.06 0.1 - 0.09 0.13 0.28
98.375 0.04 0.07 - 0.19 0.22 -
98.5 0.02 0.04 - 0.29 0.32 -
Note Eurodollars are time deposits denominated in U.S. dollars that are deposited in commercialbanks outside the U.S., and they have long served as a benchmark interest rate for corporatefunding. The Eurodollar futures contract on CME represents an interest rate on a three-monthdeposit of $1 million.
Option Premiums
Option premiums are calculated according to the value it has. The value is split into 2 parts:
Intrinsic ValueThe difference between the underlying and the strike prices
For a call option: Intrinsic Value = Underlying price - strike price
For a put option: Intrinsic Value = strike price - underlying price
Intrinsic value is always > zero
Time ValueThis is the amount of the premium which represents the risk to the writer that he option will movein the money before expiry
Time Value = Premium - Intrinsic ValueThe time value of the option is at its highest value on trade date and decreases/decays to zero onexpiry date.
Note an at the money option or out of the money option premium is entirely time value as theintrinsic value is zero.
Settling Options
Once an option has been traded a premium is payable. Further amounts are then only payable ifthe option is exercised. The nature of the settlement can either by physical or cash:
Strike prices of
futures contracts as100 - eurodollar rate
Expiry Months - the actualdate is specified by the
exchange
The premium for the option. For example the premium for a
December option with a strike price of 98.375 is $0.22
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Physical: this means that the option is actually delivered. So if the option is on an equitythe seller/writer of the option must deliver to the buyer/holder of the option the definedequity in return for cash representing the strike x number of shares agreed in the option.
Cash: For some products the physical delivery of the underlying is not feasible, forexample and interest rate option. Therefore cash is settled for the difference between themarket rate and the option rate based on the agreed notional.
It should be noted that cash settlement can also be agreed even though physicalsettlement is possible. Taking the example of the equity option again. Assume thatthe option is to buy 100 BP shares for 12 on 31/1/03. On the exercise date themarket price is 15 therefore the holder of the option exercises his right to buy butrequest cash settlement. The option writer will therefore pay the option holder 100 x(15- 12) to settle the option.
Pricing Options
The value of an option is dependent on the following factors: Strike price
Underlying price
As the price of the underlying rises the premium of a call option will increase andthe premium for a put option will fall. As the price of the underlying falls thepremium of a put option will increase and the premium of a put option will fall.
Time to expiry
The premium for an option will be higher for options with a longer period to expiryas there is more opportunity for the option to move In the Money.
Rate of movement of the underlying price - volatility
This measures the rate at which the underlying price fluctuates. It is the mostimportant factor in option valuations. Volatility is considered in terms of historicalvolatility and implied volatility.Historical volatility considers historical prices over time and is used to estimate
future volatilityImplied volatility is the future volatility level as quoted by the market.
Interest rates
These generally play a relatively insignificant role in the value of options. Thiselement relates to the cost of carry of the option - i.e. the cost of funding the optionpurchase or the opportunity cost. There is an inverse relationship. If interest ratesare falling then the premium rates will rise because the buyer of the option must becompensated for the lost opportunity of investing the option premium at higher rates
Volatility
As noted above this measures the rate at which the underlying price fluctuates. It is the mostimportant factor in option valuations. Volatility is considered in terms of historical volatility andimplied volatility.Volatilities are quoted as percentages and represent the standard deviation of the underlying. Theconfidence level of the volatility forecast being correct for one standard deviation (1) either sideof the mean is 68%, 2= 95%, 3 = 99.7%.
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For example the Euro interest rates for one year are 3.5% and the one-year volatility is forecast at10%. Therefore the standard deviation is 0.35 and for two standard deviations 0.70. Thisgives the following interest rate ranges:
Confidence Range
1 68.27% 3.15%-3.85%
2 95.45% 2.8%-4.2%
3 99.73% 2.45%-4.55%
4 99.99% 2.1%-4.9%
5 99.9999% 1.75%-5.25%
6 99.9999998% 1.4%-5.6%
Over the counter options are quoted in terms of volatility whereas XTC options are quoted interms of premiums as seen above.
The higher the volatility the higher the premium as the underlying price is more likely to moveaway from the strike price.
Margin
Margins are charged as a form of security to the exchange or broker on XTC options. They arenormally set as a percentage of the full value of the options. There are two types:
Initial margin is the amount of money, which a customer must deposit in his accountwhenever he establishes an options position. These margins must be deposited for bothlong and short positions. Initial margins normally range from 5 to 20 percent of the fullvalue of the options contracts. After depositing initial margin requirements, if the market
3.53.15 3.85
68% confidence
4.22.8
95% confidence
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moves in the customer's favour, the amount in excess of the initial margin requirementsmay either be withdrawn or used for margining additional positions.
Maintenance or variation margin. If the market moves against the customer, they will berequired to deposit additional monies in their account. This is known as maintenance orvariation margin. A maintenance margin call is issued when the customer's account valuefalls below the maintenance margin requirement, usually about 75% of the initial marginrequirement. When this happens, the customer will have to deposit sufficient funds tobring the balance in his account back up to the level of initial margin requirements.Maintenance margin calls can be met by cash deposits, deposits of Treasury Bills,transfer of funds from a related account, liquidation of positions, market appreciation orany combination of the above. During periods of extreme volatility or for very largepositions, accounts can be called for margin at any time. This type of call must usuallybe met immediately by either a wire transfer or the liquidation of positions.
Both Initial and variation margins are calculated based on the value of the portfolio, which willestablish a series of possible market movements to the option portfolio and take the worst-caseoutcome.The variation margin is calculated as follows:
These tick values are specified in the contract specifications, which are drawn up by the relevantexchanges.
Margin Calculation Methods
The most widely used is SPAN (Standard Portfolio Analysis of Risk), which applies to allLIFFE contracts, to all US futures exchanges (e.g. CME, CBOT, NYBOT) and to manyoverseas futures exchanges (e.g. MATIF, SIMEX).
Basic Trading Strategies
Each option strategy has a different profit profile. The four basic strategies are: Buy a call
Buy a put
Write/Sell a call
Write/Sell a put
These are explained below:
Buy a call
Variation Margin = number of contracts xnumber of ticks moved since last margin call x
tick value
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An investor believes that an American equity will increase in price. He does not currently havethe cash to buy the stock. Therefore he buys a European call on the stock with a strike price of
$12 three months hence. A premium of $1 is charged. The profit/value profile is: If the price of the underlying is $12 or less the option holder will do nothing. If the
holder were to exercise the option he would be buying the stock for more than he couldbuy it in the cash market. He does not exercise and he loses only the price of the option -the premium
At an underlying price of $13 the option holder exercises the option as he can now buy at
$12 and sell at $13 at a profit of $1. This offsets the premium giving a net profit of nil -known as the breakeven point.
At an underlying price of $14 the option holder makes a gain of $1 being the price atwhich underlying could be sold ($14) less the strike price at which he will buy theunderlying ($12) less the premium ($1).
The profit rises by $1 for every $1 rise in the underlying price.
Buy a put
A UK company sells products to the US. It receives payment in USD. On 1 May 2006 itreceives an order for goods worth $100,000, which will be paid for on 1 December 2006. Thecurrent exchange rate is $1.40 dollars per pound or 0.7143 pounds per dollar for which it wouldget 71,429. It buys a put option to sell dollars on 1 December for 0.7143 pounds per dollar. Thepremium is 3,000
-2
-1
0
1
2
3
4
5
6
9 10 11 12 13 14 15 16 17 18
Price of underlying
Profit/Loss
Premium.
Strike price
Out of the money In the money
Break even price $13
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If the /$ exchange rate (the underlying) is 0.7143 or more the option holder does notexercise the option as it can sell them dollars for more in the market. It loses only theprice of the option - the premium.
The breakeven point is at 0.6843 pounds to the dollar as at this point if the option holderexercises the option it will receive 71,429 giving him a net profit of 68,429 which is
the same price as if it did not have the option and sold his dollars at the current spot priceof 0.6843.
As the price of sterling to the dollar falls its gain increases.
On the other side of these buy options is the seller. Their profiles are as follows:
Sell a call
A trader sells a call to an investor who believes that an American equity will increase in price.The details are that he sells a European call on the stock with a strike price of $12 three monthshence. A premium of $1 is charged. The profit/value profile is:
Premium.
Strike price 0.7143
Out of the moneyIn the money
Break even price 0.6843
-5000
0
5000
10000
15000
20000
/$ 0.5263 0.5556 0.5882 0.6250 0.6667 0.7143 0.7692 0.8333 0.9091 1.0000
profit/loss 15,797 12,873 9,605 5,929 1,762 -3,000 -3,000 -3,000 -3,000 -3,000
1 2 3 4 5 6 7 8 9 10
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Until the investor exercises the option the trader is in profit as he keeps the premium.
Once the investor exercises the option (any price after $12) the traders profit is erodeduntil a price of $13 or more.
At a price of $15 the trader makes loss of $2, as he must sell to the option buyer for $12but has to buy in the market for $15, a loss on covering the trade of $3 against which hesets his premium of $1.
In fact the loss potential for the trader, if he does not already hold the underlying asset, is
unlimited. The writing/selling of uncovered or naked options as these are known is anextremely risky business for this reason.
Unsurprisingly the traders position is the mirror of the investors.
Sell a put
A trader sells to a UK company a put option to sell dollars on 1 December for 0.7143 pounds perdollar. The premium is 3,000
-6
-5
-4
-3
-2
-1
0
1
2
9 10 11 12 13 14 15 16 17 18
market price
profitorloss
Premium.
Strike price
Out of the money In the money
Break even price $13
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Until the company exercises the option the trader is in profit as he keeps the premium.
Once the company exercises the option (any price below 0.7143) the traders profit iseroded until a price of 0.6843 or less.
At a price of 0.5 the trader makes loss of 18,429, as he must buy $100,000 from the
option buyer for 0.7143 pounds to the dollar, which costs 71,429. The best he can sellhis dollars for is 0.5 for which he receives 50,000.
In fact the loss potential for the trader if he does not already hold the underlying asset issignificant. However in this case he is limited to the cost of the sterling of 71,429 as theprice cannot go below zero.
Again the option seller/writers position is the mirror of the buyers.
The Greeks
Each of the factors influencing the value of options is named a Greek letter as follows:
Greek Symbol Influence Calculation
Delta or Change in price ofthe underlying Change in premiumChange in Underlying Price
Gamma Change in delta Change in Delta
Change in Underlying Price
-20000
-15000
-10000
-5000
0
5000
Market rate
Profitorloss
/$ 0.5263 0.5556 0.5882 0.6250 0.6667 0.7143 0.7692 0.8333 0.9091 1.0000
Profit/Loss -15,797 -12,873 -9,605 -5,929 -1,762 3,000 3,000 3,000 3,000 3,000
1 2 3 4 5 6 7 8 9 10
Premium.
Strike price 0.7143
Out of the moneyIn the money
Break even price 0.6843
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Greek Symbol Influence Calculation
Vega (not actuallya Greek letter soalso Epsilon,Lappa)
Change in thevolatility of theunderlyinginstrument price
Change in Premium
Change in Volatility
Theta Change in time toexpiry
Change in Premium
Change in time to expiry
Rho Change in interestrate to fund theunderlyinginstrument
Change in Premium
Change in cost of funding
Creation of Contracts
Like futures exchange traded option contracts are defined by the exchange on which they are to
be traded. The following is the contract specification for the against $ Option on LIFFE. Thespecifications for any contracts can be found from the website of the exchange concerned
Unit of trading 25000
Delivery/expiry months March, June, September, December
Delivery/Exercise/expiry day Exercise on any business day. Delivery on thethird business day after the exercise day. Expiryat 17.00 on the last trading day
Last Trading Day 16.02 3 business days before third Wednesdayof expiry month
Quotations US $ per pound
Minimum price movement (tick sizeand value)
0.01cents per
($2.5)
Trading Hours 08.34-16.02
Exchange traded options are traded in a pit by brokers on an open outcry system as forfutures. Open outcry simply means that the bid and offer price and volumes are shouted out intothe pit for anyone to hear.OTC options are agreed individually between two parties, typically a bank and their client. Alldetails are agreed in writing via a confirmation.
Uses
As shown in the examples:HedgingTo provide protection against adverse price movements in the interest rate, currency andsecurities markets.
Speculation/Trading
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Making gains by buying and selling options. Profit and loss is made because of movement in theprice of the underlying.
Income and Valuation
IncomeProfit and loss is made according to value of the options, which in turn will vary according to theprice of the underlying. For an option buyer the only cost may be the premium if the option is notexercised. The option seller receives premium income. The potential costs are limitless if nakedoptions are written.
ValueExchange Trade Options: In the case of XTC options the value is the current price of the optionas quoted by the exchange, which will be, derived using the same methodologies as described forOTC options.Over The Counter Options: The valuation of options is complicated and further detailed trainingmust be obtained by anyone involved in the checking of the valuation of options. The value ofoptions depends on the following factors:
Current market price of the underlying asset - the higher the current price the more likelyit is that a call option will be exercised as the strike price is more likely to be below thecurrent price.
Strike price - the lower the strike price the more likely it is that a call option will beexercised.
Time to maturity - the longer the period to the maturity the more likely the option will beexercised as there is more time for the option to move in the money
Volatility of the underlying - this measure the extent to which the price moves. The morevolatile the underlyings price the more likely it is that the strike price will fall below themarket price in the case of a call option.
Whether the option is American or European Style - with an American style option thebuyer has more opportunity for the option to be in the money
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SECTION 2- TRADING
STRATEGIES
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Complex Trading Strategies
Complex trading strategies are combinations of two or more simple strategies.
StraddleSimultaneously buying or selling of options of different types for the same strike price
Long Straddle:- Buying a call and a put at the same time for the same strike
Long Straddle payoff
A long straddle will make losses if at the time of exercise/Expiry the strike price is nearthe market price. This is because the investor has bought exposure to both the options. Along straddle will make a profit if there is a large movement in either direction
Buy a callBuy a Put
Price of underlying
Break even - CallBreak even -put
Losses
Profits
Losses
Profits
Zero
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Short Straddle:-Selling a call and a put at the same time for the same strike
Short Straddle Payoff
The short straddle will be profitable if the underlying price is close to the strike price atthe time of expiry. If there is a large movement in the underlying price in either direction
the straddle will result into a loss
Straddle Example/Excercise
let's assume that IBM is currently trading at $100 per share. Due to a significant eventthat will occur this month (an expected news event, earnings release, etc.), an investormight believe that the stock will move at least 10% in either direction. In this example,let's assume that both the IBM 100 put options and IBM 100 call options are trading at $3each. To take advantage of this the investor would enter into a straddle trade bypurchasing both the IBM 100 put for $3 and the IBM 100 call for $3 (for a total of $6 out
of pocket).
Draw the payoff diagram of the straddle
Calculate the profit or loss if
The market price had risen 10%
Losses
Profits
Sell a put
Sell a Call
Strike Price
Profits
Losses
Underlying priceZero
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The market price had fallen by 15%
If the market price moved by 2 %
Reasons for trading the straddle
Investor is trading on volatility. A long straddle useful when the investor is expecting a large movement in
underlying price in either side but is not sure which direction the same will be in. A short straddle will be useful when the investor is expecting a small movement
in the underlying price in either of the directions
StrangleDefinition: - Buying or selling of option of different types with different strikes
Long Strangle: - Buy a call with high strike price and put with low strike price
Profit Profile
Call break even
Put StrikeCall Strike
Put break even
Underlying price
Losses
Profits
zero
Buy a put
Buy a call
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A long strangle will make a profit if there is a large movement in the price of theunderlying in the either direction. If the underlying price is in between the two prices orclose to the same the strangle will lead to a loss
Short Strangle
Sell a call with high strike and a put with low strike
Short Strangle Payoff
A short strangle will be profitable if the underlying price is close to or in between the twostrike prices. However if there is a large movement in the underlying price in either of thedirection a short strangle position will be at a loss
Reasons for trading in Strangles
Investor is trading on volatility. A long straddle useful when the investor is expecting a large movement in
underlying price in either side but is not sure which direction the same will be in. A short straddle will be useful when the investor is expecting a small movement
in the underlying price in either of the directions The underlying price movement has to be greater than in case of a strangle, hence
the premium paid by the buyer of the strangle will be lower
Put Break even Put Strike Call strikeCall break even
Losses
Profits
zero Underlying price
Sell a call
Sell a put
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Strangle Example/Excercise
Reliance is currently trading at 325. The investor expects a big jump in prices due to de
- merger of the company but is not sure how the same will affect the price He buys a callat 360 and a put at 300. He pays a premium of Rs.10/share on call and 5/share on put.The contract size is 200 shares.
Answer the following
1. When will the investor start making profit?
2. When will he make a loss?
3. What is his breakeven point?
4. If at the time of expiry reliance was trading at the following prices calculate netprofit or a loss
a. 380b. 370c. 350d. 335e. 310
Spreads
Definition- Buying or selling of options of the same type with different strike price
Long Call Spreads:- Buy a call with low strike price and sell a call with high strike price.Also known as bull call spreads. The expiry and the underlying should be same
Bull spreads have limited profit potential. The risks are also limited to the premium paid
Bull call spread Payoff
A bull call spread will be profitable if the underlying price is greater than the breakevenpoint. The breakeven point for the bull call spread will be the lower strike + premium.This can be better explained by way of an example
Assume XYZ Stock is trading at 102.50. You buy 1 XYZ Apr 100 call at a premium ofRs.9 and sell XYZ Apr 110 call at Rs.5.
The net cost of the spread is Rs.4.
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The maximum risk is Rs.4.The maximum gain will be the spread (110-100) premium = Rs.6.
Breakeven point will be at 104 ( Lower strike + premium).
If the price remains at 102.50 the investor will exercise the call hence will gain 2.5. Thebuyer of the high strike will not exercise the call. This will result in a total loss of 1.5
If the market price is 108 again the investor will exercise the long call and gain Rs.8 Theshort call will not be exercised. Resulting in a net profit of 8-4 = Rs.4
If the price is 99 neither options will be exercised resulting in a net loss of 4
If the price is more than 110 both the long and the short calls will be exercised. Theinvestor will pay and receive on both hence the maximum gain the investor can have is 6.
Reasons for trading in Bull spreads
Investor expects that the price will rise up to a certain level Wants to minimize the premium cost.
Buy a Call
Losses
0
Profits
Sell a Call
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Log Put Spread:- Buy one put with high strike price and sell another put with a lowstrike price. The expiry and the strike for both should options being the same. Long putspreads are also called bear spreads.
Bear spreads have limited profit potential. The risks are also limited to the premium paid
Bear Spread payoff
The payoff from the long put spread can be better understood by way of an example.
QRS stock is currently trading at 63.75 an investor is expecting a fall in the prices from63.75 to 60.00 hence he buys a bear spread. He buys a put at 65 premium of 5.5 and sellsa put at 60 for a premium of 3.25.
The net cost of the put to the investor is 2.25
The Maximum gain will be spread minus the premium = 2.75
Breakeven will be higher strike premium
If on the expiration date the stock is trading at 63.75 the long put will beexercised. The gain from the same will be 1.25. The net loss will be 1.00. The
0
Profits
Buy a Put
Sell a put
Losses
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short put will not be exercised as the strike price is less than the market price,hence option is not in the money.
At 62.75 There will be no profit no loss
AT 60.00 The long put will be exercised. The gain from exercise being 5. Netprofit being 2.75
At 59 both the puts will be exercises and the investor will pay on one put andreceive on another
o On long call he received 6o On short call he pays 1o Net receipt 5o Less the net premium paid of 2.25o Net gain of 2.75
Thus his profits are limited to 2.75.
Reason .for trading in Bear Spreads
Investor expects that the price will rise up to a certain level Wants to minimize the premium cost.
Spreads Exercise
1. How is a bull call spread created?
1. Buy a short-term call and sell a long-term call2. Buy a call with a higher strike price and sell a call with a lower strike price3. Buy a call with a lower strike price and sell a call with a higher strike price
2. Which of the following is an example of a bear put spread?
1. Buy 1 CDE Aug 120 put @ 7.50Sell 1 CDE Aug 110 put @ 4
2. Buy 1 LMN 85 put @ 2Sell 1 LMN 90 pt @ 3.75
3. Buy 2 JQQ 35 puts @ 2.25Sell 1 JQQ 40 put @ 5
3. Assume you purchase the following bull call spread:Buy 1 STS 40 call 3.75Sell 1 STS 45 call 1.75
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4. If the price of STS stock is $39 at expiration, what is the profit or loss fromthis bull call spread?
1. Profit of 32. Profit of 23. Loss of 2
4. Loss of 3.75
5. Assume you purchase the following bear put spread:Buy 1 EFG May 95 put @ 6.50Sell 1 EFG May 85 put @ 2.25If the price of EFG stock is $84 at expiration, what is the profit or loss fromthis bear put spread
1. Profit 6.502. Profit 5.753. Loss 4.25
4. Loss 2.25
6. Assume you purchase the following bull call spreadBuy 1 ABC Nov 60 call 5.75Sell 1 ABC Nov 65 call 3.50If the price of ABC stock is $64 at expiration, what is the profit or loss fromthis bull call spread?
1. Profit 2.752. Profit 1.753. Loss 2.254. Loss 2.75
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SECTION 2- Exotic Options
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Average/Asian options
Definition:- An option whose payoff depends on the average of the underlying over thelife of the option
Can beAverage Price:- The payoff is difference between the strike and average of theunderlying price.
Average Strike:- An option where the strike rate equals the average of the underlyingindex over the life of the option. The Strike is not set on onset. It is derived as the averageof the underlying price. On expiration the current underlying price is compared with theaverage calculated and the payoff is determined
Example:-
A multinational GBP based company has a large flow of foreign currency receipts overthe year. While each individual receipt is difficult to forecast and only small, over theyear the total USD income equals in excess of USD 25 million. The current spot rate is1GBP = 1.50USD. Given the random timing of the cashflows and the small individualsize, traditional FX options have proved to be impractical. The company can considerusing an Average Rate Strike Option. The company is comfortable that the total incomein one year will exceed USD 25 million. The company could purchase a 1 yr USD 25mmWeekly Average Strike Rate Put option at say 1.75%. Each week the USD/GBP spot ratewould be noted from an agreed source at an agreed time. The strike rate for the option isthen set at the end of the year at the calculated average rate and used to calculate the
value of the option:
USD 25,000,000 * (Spot at Maturity - Average Strike) * days/365
Assuming the average strike equals 1.43 and the USD/GBP spot rate at maturity is 1.60,the option payout would equal:
USD 25,000,000 * (1.60 - 1.43) * 365/365 = USD 4,250,000 or GBP 2,656,250
The company achieves a general hedge against a falling USD at a reasonable cost.
Advantages
Lower premium Customised General protection of small regular cash flows Accurate reflection of the underlying price over a period.
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Useful ways of protecting a series of cash flows against rate moves when thedates of receipts cannot be accurately predicted.
Disadvantages
General protection rather than specific
Barrier Option
Definition:-Barrier options are a family of options that either come alive or die whenpredetermined trigger points (barriers) are reached. Most available options can be adaptedto be barrier options
There are two major types
Knock Ins and Knock Outs.
Knock In options come alive when the barrier is reached. They can be
Down and in: - Will come alive when the underlying price falls to a barrier level
Up and in: - Will come alive when the underlying price rises to the barrier level
Knock out options die when the barrier is reached.
Down and out: - Will die when the underlying price falls to a barrier level
Up and out: - Will die when the underlying price rises to the barrier level
The barrier can be any tradable variable and may or may not be directly related to theunderlying of the original option.
These can be call or a put
These can be either European or American options
The Barrier can be either
Inside Barrier: - Where the barrier relates to the price of the underlying asset
Outside side barrier: - Where the barrier relates to price of another asset
Pricing
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The price of a barrier option depends upon the probability of the barrier being reached,and the value of the underlying option if it is reached. They are therefore very sensitive tovolatility.
Advantages
Cheaper than standard options Flexibility in setting the barrier level and thus the cost of the option Can be linked to any underlying Customised to clients exposures
Disadvantages
The rate protection is contingent upon an "independent" event
Binary options
Payout in case is fixed amount if the option is in the money at the time of expiration.Binary is zero or one, there are only two possibilities. Similarly in binary options if theoption is in the money at the time of expiry then a fixed sum is paid. The level ofunderlying is irrelevant. They are also known as digital option
Digital Options are relatively common. As volatility increases the digital options becomecheaper compared to the conventional options as the there is only a fixed payout
Digital options can be
Cash or nothing - Where the cash is paid if the option is in the money
Asset or nothing: - Payoff is an asset if the option is in the money
One Touch Digital: - If the barrier is reached anytime during the life of the option thenbuyer receives the payout 2 days after the expiry
Instant one touch: - Buyer received a payout 2 days after the barrier is reached
Digital Knock in: - Combination of digital and knock in. A fixed payoff if the option is inthe money at the time of expiry and the barrier has been reached
Digital Knock out: - Combination of digital and knock out. A fixed payoff if the option isin the money at the time of expiry and the barrier has not been reached
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Ladder Options
Definition :- With a Ladder option, the strike is periodically reset when the underlyingtrades through specified trigger levels, at the same time locking in the profit between theold and the new strike.
The trigger strikes appear as rungs on a ladder. Ladder options can be structured to resetthe strike in either one or both directions. The Ladder option is also known as a Ratchetoption and Lock-In option.
Example
An investment fund that is bullish on the USD wants to buy USD calls. If the fund buys aEuropean call it can only exercise the option at the maturity date. If it buys an Americancall though, it will face the problem of when to exercise the option. The fund decides tobuy a Ladder Option with a strike of 1.65 and a ladder with rungs starting at 1.65, going
upwards in steps of 5 pf to a maximum of 1.80. Now every time USD/DEM reaches anew rung, the strike will be reset to that rung and a 5 pf profit locked in. So if during thelifetime of the deal USD/DEM reaches its high at 1.7620, the highest rung reached willbe 1.75 and the strike will thus be set accordingly, while the profit of 10 pf (1.75-1.65)will be locked in. At expiry the fund will receive the greater of (a)closing spot lessoriginal strike, and (b) highest rung reached less original strike. If in our example, thehighest level was 1.7620 but the rate closes at 1.53, the fund will receive 10 pf only. Ifhowever the spot closes at 1.762, the fund will receive 11.2 pf.
Pricing
A Ladder Option can be viewed as a series of Knock-In and Knock-Out call and putoptions each struck at a different ladder level. Our above example is made up bycombining a 165 call and a series of bought and sold Knock-In Puts (see "FX Knock-InOptions").
Advantages
Less risky than traditional options as profits locked in as underlying performs No need to constantly watch the underlying market levels Ladder options are applicable for risk averse option buyers as profits are
progressively locked in without losing the option position.
Disadvantages
More expensive than a normal option
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Cliquet Options
Defination :- A Cliquet Option settles periodically and resets the strike at the then spot
level.
It is therefore a series of at-the-money options, but where the total premium is determinedin advance. A Cliquet can be thought of as a series of "pre-purchased" at-the-moneyoptions. The payout on each option can either be paid at the final maturity, or at the endof each reset period.
Example
A three year Cliquet Call on the FTSE with annual resets is a series of three annual at-the-money spot calls. The initial strike is set at say 3000. If at the end of year one, the
FTSE closes at 3300, the first call matures 10% in-the-money and this amount is paid tothe buyer. The call strike for year 2 is then reset at 3300. If at the end of year 2, the FTSEcloses at 2900, the call will expire worthless. The call strike for year 3 is then reset at2900. The alternative strategy would be to buy a one year at-the-money call and at theend of year one, buy another at-the-money one year call, and so on. The difference is thatthe cost of the Cliquet is known in advance, whereas the future cost of at-the-money callsis unknown. If volatility is LOWER than expected, the Cliquet will be more expensivethan buying the calls annually, if volatility is HIGHER than expected, the Cliquet will becheaper. A Cliquet option is therefore more attractive when volatility is expected toRISE.
The major advantage of the Cliquet, is that the probability of some payout is high. Overthe 3 year period, the chance that the market will close lower for three consecutive years,is much lower than the probability that the market will close lower at the END of threeyears i.e. there is a high probability that even if the market closes lower after three years,that it will have closed higher in at least one of the three years.
Pricing
A Cliquet is a series of at-the-money options. We can calculate the expected value ofthese options by generating the implied forward volatility curve (some methodology asgenerating implied forward interest rates. See "Implied Forwards"). The Cliquet premium
is the present value of the premiums for the option series. A Cliquet call is always moreexpensive than a straight at-the-money call with the same final maturity.
The number of reset periods is determined by the buyer in advance. More resets make theoption more expensive. A Coupe is a cheaper alternative to the Cliquet (see "CoupeOptions").
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The Cliquet is suitable for investors with a medium term investment horizon. It is lessrisky than ordinary medium term options, as there is less specific risk i.e. the reset facilitygives the buyer a "second" and "third" chance. This increases the chance of payout, butmust be balanced with the higher premium cost. As a series of "pre-purchased" options,the Cliquet is attractive to passive investors as it requires no intermediate management.
They have traditionally been attractive to retail and private investors when embedded indeposits and bonds (see "Structured Assets ") as they provide a low risk (capitalguaranteed) exposure to equity and Bond markets. Sophisticated investors use Cliquets totake advantage of future assumptions about volatility.
Advantages
There is a "second chance" as the strike is periodically reset Ideal medium term, passive investment Locks in the future cost of volatility
Disadvantages
More expensive than straight options with same final maturity
Lookback Options
Definition: - At maturity the buyer can "lookback" and set the most favorable strike tomaximize profit between strike and maturity. Lookback Options are also known asHindsight Options.
There are two types of Lookback option:
Set a strike at the start: - At maturity, the buyer can "lookback" over the life of the optionand choose the most favorable exercise point to maximize profit between strike andexercise.
Set a strike at maturity: - At maturity the buyer can "lookback" and set the mostfavorable strike to maximize profit between strike and maturity. Lookback Options arealso known as Hindsight Options.
Example
An investor expects a sharp rise in the CAC 40 over the next year. A straight 1 year callwith an at-the-money spot strike of 1900 would cost 236 points. A Lookback call strike1900 would cost 343 points but would give the investor the opportunity to lookback atmaturity and select the highest point reached by the CAC 40 as the exercise point thusmaximizing profit. If the CAC 40 is higher than 1900 at any time over the year, theinvestor is assured of some payout. The lookback feature is thus very attractive to
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investors as it gives the buyer the best possible payout. However, Lookback options aregenerally very expensive.
Pricing
Since the option will always choose the highest profit available, the major determinant ofthe option price will be the volatility of the underlying. The more volatile the underlying,the higher the probability that the underlying will move dramatically enough to allow theinvestor a significant profit, therefore the higher the volatility the more expensive theLookback.
Lookback Options are applicable for risk averse investors unsure about timing of themove in the underlying. They are lower risk as there is a high probability of return.However, they do involve a larger upfront premium.
Advantages
The buyer will always be able to lock in the most favorable profit that appearedduring the life of the option
Disadvantages
The Lookback Option will require higher premiums than conventional options