MMS Derivatives Lec 1

7/30/2019 MMS Derivatives Lec 1

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Introduction to Derivatives

By Vaibhav KabraM.F.S.M, F.R.M.


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1 Introduction to Derivatives

2 Forwards & Futures Contracts and their Payoffs

3 Hedging with Futures(Not included)

4 Pricing Futures & Forwards (Not included)

5 Options Contracts and their Payoffs

6 Options Strategies

7 Pricing Options (Not included)

Index


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The Nature of Derivatives

A derivative is an instrument whose value

depends on the values of other more basic

underlying variables

Asset - Equity, Bonds, Commodity

Rate - Index, Interest Rate, Fx Others - Energy, Weather & Insurance


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Examples of Derivatives

Futures Contracts Forward Contracts Swaps Options


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Derivatives Markets

Exchange traded Traditionally exchanges have used the open-outcry

system, but increasingly they are switching toelectronic trading

Contracts are standard there is virtually no credit risk

Over-the-counter (OTC) A computer- and telephone-linked network of dealers at

financial institutions, corporations, and fund managers

Contracts can be non-standard and there is some smallamount of credit risk


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Ways Derivatives are Used

To hedge risks

To speculate (take a view on the future direction of

the market)

To lock in an arbitrage profit

To change the nature of a liability

To change the nature of an investment without

incurring the costs of selling one portfolio and buying

another


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Forwards & Futures Contracts andtheir Payoffs


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Forward & Future Contracts

A Forward Contractis a bilateralcontract traded in the OTCMarket that obligates one party to buy and the other party to sell aspecific quantity of an asset, at a set price, on a specific date infuture.

AFutures Contract

is a bilateralcontract traded in an Exchangethat obligates one party to buy and the other party to sell a specificquantity of an asset, at a set price, on a specific date in future.

The buyer of the contract is called as the holder of the LongPosition.

The seller of the contract is called as the holder of the ShortPosition.


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Forward & Future Contracts

If the expected future price of the asset increases over the life of thecontract, the long position (buyer) will have a positive value and theshort position (seller) will have an equal negative value.

If the expected future price of the asset decreases over the life of thecontract, the short position (seller) will have a positive value and thelong position (buyer) will have an equal negative value.

More often, a party seeks to enter into a forward contract to hedge a

risk it already has.

The forward contract is used to eliminate uncertainty about thefuture price of an asset it plans to buy or sell at a later date.


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Stock Price100 110102 1059890 950

2

5

10

-2

-5

-10

Pay Off

Pay Off for the Buyer

Pay off for the Buyer

= (SX)

= ($105-$100).. ( S > X)

= $5

= ( $95-$100) ( S < X)

= - $5


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100 110102 1059890 950

2

5

10

-2

-5

-10

Stock Price

Pay Off

Pay Off for the Seller

Pay off for the Seller

= (XS)

= ($100-$95).. ( X > S)

= $5

= ( $100-$105) ( X < S)

= - $5


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Over The Counter (OTC) Markets

A decentralized market where market participants trade over the

telephone, facsimile or electronic network instead of a physical

trading floor. There is no central exchange or meeting place for this

market.

The contracts in the OTC Market are privately traded The contracts are non standardized and decided as per mutual

agreement between the two counterparties entering the contract.

Unlike the Exchange, generally there are no margin requirements in

the forward contracts that are initiated in the OTC Market. As there are no margin requirements and no centralized exchange

involved, the probability of default of the loosing counterparty is

higher.


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Futures ContractsSpecifications

Standardization

Underlying Asset: The exchange specifies the quality of goods thatcan be delivered. i.e. The exchange stipulates the grade or grades ofthe commodity that are acceptable.

Contract Size: The contract size specifies the amount of the assetthat has to be delivered under one contract. The contract size has tobe optimum. i.e. the contract size can not be too large nor can it betoo small.

Delivery Arrangements/Location: The place where the deliverywill be made must be specified by the exchange

Delivery Months: The Exchange must specify the precise periodduring the month when delivery can be made.


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Price Quotes: The exchange also sets the minimum pricefluctuations

Price Limits: Contracts also have a daily price limit, which sets the

maximum price movement allowed in a single day

Position Limits: Position Limits are the maximum number ofcontracts that a speculator may hold. The purpose of the limits is toprevent speculators from exercising undue influence on the market.

Futures ContractsSpecifications

Standardization


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Clearing House

Each exchange has a clearing house

The clearing house guarantees that traders in the futures market willhonor their obligations

The clearing house does this by acting as an opposite side of eachposition. The clearing house acts as a buyerto every sellerand a

sellerto every buyer By doing this, the clearing house allows either side of the trade to

reverse positions at a future date without having to contact the otherside of the initial trade

This allows traders to enter the market knowing that they will be

able to reverse their position Traders are also freed from having to worry about the counterpartydefaulting since the counterparty is now the clearing house

In the history of US Futures trading, the clearing house has neverdefaulted.


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Futures Contracts- Characteristics

Margin Requirements

Initial Margin is the money that must be deposited in a futuresaccount before any trading takes place. i.e. Initial Margin must bedeposited in the margin account at inception.

Maintenance Margin is the amount of margin that must be

maintained in a futures account. If the margin balance in the accountfalls below the maintenance margin, additional funds must bedeposited to bring the margin balance back to the initial marginrequirement.

Variation Margin is the funds that must be deposited into theaccount to bring it back to the initial margin amount.

Initial and Maintenance Margins are set by the clearing house andare based on historical daily price volatility


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Closure of

Forwards & Future Contracts

Delivery: A short can terminate the contract by delivering the

goods, a long by accepting delivery and paying the contract price to

the short. The location for delivery, terms of delivery and details of

exactly what is to be delivered are all specified in the contract.

Cash Settlement: The futures account is marked to market based on

the settlement price on the last day of trading.

Terminating a position Prior to Expiration: A party to a forwardor a future contract can terminate the position prior to expiration by

entering into an opposite contract.


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Difference: Forwards & Futures

Forward Contracts Future Contracts

Privately Traded contracts Over the

Counter

Traded on the Exchange

Highly Customized, NonStandardized Contracts Specifications are provided by theexchange, hence Standardized

Contracts

No Marking to Market Requirements

i.e. No Margins required

Marking to Market Requirements i.e.

Margins are required

Delivery or Final cash settlement

usually takes place

Contract is usually closed prior to

Maturity

As there is some probability of

default, Credit Risk exists

As there is no probability of default,

Credit Risk does not exist


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Concept Checkers

The short in a deliverable forward contract:

a) Has no default risk

b) Receives a payment at contract initiation

c) Is obligated to deliver the specified asset

d) Makes a cash payment to the long at settlement

On the settlement date of a forward contract:

a) The short may be required to sell the asset

b) The long must sell the asset or make a cash payment

c) At least one party must make a cash payment to the other

d) The long has the option to accept a payment or purchase the asset


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Concept Checkers

An investor enters into a short forward contract to sell 100,000

British Pounds for US dollars at an exchange rate of 1.5 US

dollars per pound. How much does the investor gain or loose of

the exchange rate at the end of the contract is

a) 1.49 b) 1.52

A trader enters into a short cotton futures contract when the

futures price is 50 cents per pound. The contract is for thedelivery of 50,000 pounds. How much does the trader gain or

loose if the cotton price at the end of the contract is

a) 48.20 cents per pound

b) 51.30 cents per pound


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Concept Checkers

The daily process of adjusting the margin in a futuresaccount is called :

a) Initial Margin

b) Variation Margin

c) Marking to Marketd) Maintenance Margin

Funds deposited to meet a margin call are termed :a) Variation Margin

b) Daily Margin

c) Loan Payments

d) Settlement Costs


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Concept Checkers

Compared to forward contracts , futures contracts are least likely to be :a) More liquid

b) Standardized

c) Larger in Size

d) Less Subject to default risk.

An investor enters into a short position in a gold futures contract at$294.20. Each futures contract controls 100 troy ounces. The initialmargin is $ 3200 and the maintenance margin is $ 2900. At the end ofthe first day, the futures price drops to $ 286.60. Which of the followingis the amount of the variation margin at the end of the first day?

a) $0

b) $34

c) $334

d) $760


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Options Contracts and their Payoffs


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Option Contracts

An Option Contractgives the Owner the right, but not the

obligation, to buy or sell the underlying from the seller of the

Option.

A Call Option gives the Owner the right, but not the

obligation, to Buy the underlying from the Seller of the

Option.

The Call Option Owner is also called the Buyer or the holder

of the Long position

The Call Option Seller is also called the Writer or the holder

of the Short position


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A Put Option gives the Owner the right, but not the obligation,

to Sell the underlying from the seller of the Option.

The Put Option Owner is also called the Buyer or the holder

of the Short position

The Put Option Seller is also called the Writer or the holder of

the Long position


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Payoffs of Call & Put Options

S = Price of the underlying asset

X = Strike price

C = Market Value of the Call Option

P = Market Value of the Put Option

Unlike Forwards and Futures contracts, Optioncontracts have asymmetric Payoffs


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100 110102 1059890 950

2

5

10

Pay Off

Stock Price

Payoff for a Call Buyer

C = SX if S > X

C = 0if S


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100 110102 1059890 950

-2

-5

-10

Stock Price

Pay Off

Payoff for a Call Seller

Payoff for a Call Seller

C = -(SX) if S > X

C = 0if S X

= C0 if S


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Intro to Derivatives 30

100 110102 1059890 950

2

5

10

Stock Price

Pay Off

*** Option Premium Calculation is not included in this slide

Payoff for a Put Buyer

P = XS if X > S

P = 0if X


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Stock Price

100 110102 1059890 950

-2

-5

-10

Pay Off Payoff for a Put Seller

Payoff for a Put Seller

C = -(XS) if X > S

C = 0if X S

= P0 if X


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Consider a call option selling for $7 in which the exercise price is $100

and the price of the underlying is $98.

A. Determine the value at expiration and the profit for a buyer under the

following outcomes:

The price of the underlying at expiration is $102

The price of the underlying at expiration is $94B. Determine the value at expiration and the profit for a seller under the

following outcomes:



C. Determine the following The maximum profit to a buyer (maximum loss to the seller)

The maximum loss to a buyer (maximum profit to the seller)

D. Determine the breakeven price of the underlying at expiration


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Consider a put option selling for $4 in which the exercise price is $60 and

the price of the underlying is $62.

A. Determine the value at expiration and the profit for a buyer under the

following outcomes:



B. Determine the value at expiration and the profit for a seller under the

following outcomes:



C. Determine the following The maximum profit to a buyer (maximum loss to the seller)

The maximum loss to a buyer (maximum profit to the seller)

D. Determine the breakeven price of the underlying at expiration


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Moneyness of an Option

Calls are in the money when the value of the underlying exceeds theexercise price

Puts are in the money when the exercise price exceeds the value of

the underlying

Calls are out of the money when the value of the underlying is lessthan the exercise price

Puts are out of the money when the exercise price is less than thevalue of the underlying

One would notnecessarily exercise an in the money option. But onewould neverexercise an out of the money option


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Option Price

Option Price = Intrinsic Value + Time Value

Intrinsic Value consists of the value of the option if exercisedtoday.

Intrinsic value of a call is max [(SX) , 0] Intrinsic value of a put is max [(XS) , 0]

Time Value or Speculative Value consists of the remainder,reflecting the possibility that the option will create further gains in

the future.

The longer the time to expiration, the greater the time value andhence the greater the Options Premium.

At expiration, there is no time remaining and hence the time value iszero.


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Factors affecting Option Prices

Factor American

Call

American Put European Call European Put

Stock Price

S

Strike PriceX

Time to

expiration T

Volatility

Dividend D

Risk free rate

r


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Portfolio Position Initial

Payoff

ST < X ST >= X

1 Buy Call -c 0 STX

Sell Put +p -(XST) 0

Invest -Xe-rT X X

Total -c+p-Xe-rt ST ST

2 Buy Asset -S ST ST

Put Call Parity-Equation

European Options (Non Dividend Paying)


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Payoff for a Put SellerPayoff for a Call Buyer

Long Asset


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The portfolio consists of a long position in the call

A short position in the put

an investment to ensure that we will be able to pay the exercise price

at maturity.

Long positions are represented by negative values as they areoutflows.

The Put Call Parity equation is given as :

P + S = c + Xe-rt

The above equation holds true only for European Style Options. Also,

the puts and calls must have the same exercise price for these

relations to hold.


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Other Synthetic Equivalents of Put Call Parity

Equation

S = cp + Xe-rt

p = cS + Xe-rt

c = S + pXe-rt

Xe-rt = S + p - c




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Lower Bound of European Calls

(Non Dividend Paying Stock)

Portfolio A: One European Call Option + an amount of cash equal

to X e-rt

Portfolio B: One Share

At Option Maturity:

Portfolio ST < X ST > X

Portfolio A X ST

Portfolio B ST ST

Max (ST, X)

ST

Hence, Portfolio A is always worth as much as, and can be worth more than,

portfolio B at the options maturity.


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C + X e-rT >= S0

C >= SOX erT

A call value can never be negative. Therefore

C >= max(S0X e-rT , 0)


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Lower Bound of European Puts


Portfolio C: One European Put Option + One Share

Portfolio D: An amount of Cash equal to X e-rT

At Option Maturity:


Portfolio C X ST

Portfolio D X X

Max (ST, X)

X

Hence, Portfolio C is always worth as much as, and can be worth more than,

portfolio D at the options maturity.


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P + S0 >= X e-rT

P >= X e rT - SO

A put value can never be negative. Therefore

P >= max (X e-rT - S0 , 0)


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Early Exercise of American Calls


The holder gets exactly STX if the option is exercised early.

However, C >= SOX erT is strictly greater thanSTX

Hence, an American Call on a non dividend paying stock

should never be exercised early.

The only reason to exercise early a call is to capture a dividend

payment. Therefore, a high income payment makes holding

the asset more attractive than holding the option.

Thus American Calls on income-paying assets may be

exercised early.


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Early Exercise of American Puts


The holder gets exactly X - ST if the option is exercised early.

However, X - ST is strictly greater thanP >= X e rTSO

Hence, an American Put on a non dividend paying stock should

always be exercised early.

Because it is better to receive money now than later, it may be worthexercising the put option early.

Thus American Puts on non income-paying assets may be exercised

early.

The probability of early exercise decreases for lower interest ratesand with higher income payments on the asset. In each case, it

becomes less attractive to sell the asset.


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Lower and Upper Bounds for Options

Option Lower Bound

(Minimum Value)

Upper Bound

(Maximum Value)

European Call CE > = max (0,S0X e-rT ) S0

American Call CA > = max (0,S0X e-rT ) S0

European Put CE > = max (0, X e-rT - S0 ) X e

-rT

American Put CA > = max (0, X - S0 ) X


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(Dividend Paying Stock)

Portfolio A: One European Call Option + an amount of cash equal

to D + X e-rt

Portfolio B: One Share

At Option Maturity:


Portfolio A D + X ST + D

Portfolio B ST ST

Hence, Portfolio A is always worth as much as, and can be worth more than,

portfolio B at the options maturity.


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C + D + X e-rT >= S0

C >= SOD - X erT

A call value can never be negative. Therefore

C >= max(S0D - X e-rT , 0)




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Portfolio C: One European Put Option + One Share

Portfolio D: An amount of Cash equal to D + X e-rT

At Option Maturity:


Portfolio C X ST

Portfolio D D + X D + X

Hence, Portfolio C is always worth as much as, and can be worth more than,

portfolio D at the options maturity.


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P + S0 >= D + X e-rT

P >= D + X e rT -SO

A put value can never be negative. Therefore

P >= max (D + X e-rT - S0 , 0)




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Put Call Parity

Put Call Parity for Dividend Paying European Options:

C + D + X e-rT= P + S0

Put Call Parity for Non Dividend Paying American Options:(S0X)


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Concept Checkers

Which of the following statements about moneyness is least

accurate ? When :

a) S - X is > 0 , a call option is in the money

b) S - X is = 0 , a call option is at the money

c) S = X , a put option is at the money

d) S > X is > 0 , a put option is in the money


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Concept Checkers

Which of the following statements about put and call option is leastaccurate ?

a) The price of the option is less volatile than the price of the underlying stock.

b) Option prices are generally higher the longer the time till the option expires .

c) For put options , the higher the strike price relative to the stocks underlyingprice , the more put is worth.

d) For call options , the lower the strike price relative to the stocks underlyingprice , the more call option is worth.

Which of the following statements about American and Europeanoptions is most accurate ?

a) There will always be some price difference between American and European

options because of exchangerate riskb) American options are more widely traded and are thus easier to value.

c) European options allow for exercise on or before the option expiration date

d) Prior to expiration , an American option may have higher value than anequivalent European option.


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Concept Checkers

Which of the following statements is most accurate ?a) The writer of a put option has the obligation to sell the asset to the holder of

the put option.

b) The holder of the call option has the obligation to sell the option writershould the stocks price rise above the strike price.

c) The holder of the call option has the obligation to buy from option writer

should the stocks price rise above the strike price.d) The holder of the put option has the right to sell to the writer of the option.

A $40 call on a stock trading a $43 is priced at $5. The time value of theoption is :

a) $2b) $3

c) $5

d) $8


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Concept Checkers

Which of the following will increase the value of a putoption

a) An increase in Rfb) An increase in volatility

c) A decrease in the exercise price

d) A decrease in time to expiration

The lower bound for a European put option is :a) Max (0,S-X)

b) Max (0,X-S)c) Max (0,Xe-rt-S)

d) Max (0,S-Xe-rt)


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Concept Checkers

Which of the following relations is least likely accurate ?a) S=C-P+Xe-rt

b) P=C-S+Xe-rt

c) C=S-P+Xe-rt

d) Xe-rt-P=S-C

The lower bound for an American call option is :a) Max (0,S-X)

b) Max (0,X-S)c) Max (0,Xe-rt-S)

d) Max (0,S-Xe-rt)


59/85

Concept Checkers

According to the put call parity, writing a put is likea) Buying a call, buying stock and lending

b) Writing a call, buying a stock, and borrowing

c) Writing a call, buying a stock, and lending

d) Writing a call, selling stock, and borrowing

Given strictly positive interest rates, the best way to closeout a long American call option position early would be to

a) Exercise the call

b) Sell the callc) Deliver the call

d) Do none of the above


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Concept Checkers

Which of the following statements about options on futuresis true

a) An American call is equal in value to an European Call

b) An American put is equal in value to an European Put

c) Put-Call Parity holds for both American and European Options

d) None of the above statements is true

Given strictly positive interest rates, the best way to closeout a long American call option position early would be to

a) Exercise the callb) Sell the call

c) Deliver the call

d) Do none of the above


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Options Strategies


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Covered Calls

The Covered Call is constructed by combining a long position in astock plus a short position in a call option.

The long position covers or protects the investor from the payoff onthe short call that becomes necessary if there is a sharp rise in thestock price.

Also, if the investor already owns the stock, this strategy is used togenerate cash on the stock that is not expected to increase above theexercise price over the life of the option.


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Long Asset

0

Short Call

Covered Call


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Protective Puts

The protective put is constructed by holding a long position in theunderlying security plus buying a put option.

Protective Put is used to limit the downside risk at the cost of PutPremium.

The investor will be able to benefit from the increase in the stockprice, but it will be lower by the amount paid for the put.


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Long Asset

Protective Puts

Buy Put


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Bull Call

Construction: Buy a call option with a low exercise price, XL Subsidize the purchase price of the call by selling a call with a higher

exercise price, XH.

Whats in the Investors mind?

This strategy is a bull strategy.

The investor wants to benefit himself from rising stock prices

The buyer of a bull call spread expects the stock price to rise and thepurchased call to finish in the money.

However, the buyer does not believe that the price of the stock will rise

above the exercise price for the out of the money written call

Equation:

Profit = max (S-XL , 0)CLmax (S-XH , 0) + CH


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Bull Put

Construction: Sell a put option at a higher Strike Price, XH Buy a put option at a Lower Strike Price, XL.


This strategy is a bull strategy.

The investor wants to benefit himself from rising stock prices

The buyer of a bull put spread expects the stock price to remain above XH The buyer buys the put at a Lower Strike Price to protect himself from

steep decline in the Stock Price

Equation:

Profit = max (XL- S , 0)PLmax (XH -S, 0) + PH


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Bear Call

Construction: Sell a call option with a low exercise price, XL Buy a call option at a higher Strike Price, XH.


This strategy is a bear strategy. The investor wants to benefit himself from falling stock prices

If the stock prices fall, the investor profits from the premium of the writtencall

The intention to buy a call option is to protect himself from steep rise instock prices

Equation:

Profit = max (S-XH , 0)CHmax (S-XL , 0) + CL


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Bear Put

Construction: Sell a put option at a Lower Strike Price, XL Buy a put option at a Higher Strike Price, XH.


This strategy is a bear strategy. The investor wants to benefit himself from falling stock prices

Therefore he purchases a put option at a Higher Strike Price Also, he believes that the prices will not fall below XL . Therefore he sells a

put option at XL and keeps the premium for himself. In other words, he hassubsidized the put option that he has bought.

Equation:

Profit = max (XH-S , 0)PHmax (XL -S, 0) + PL

fl d i


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Butterfly Spreads using

Call Options

Construction:

Buy a call option at a Lower Strike Price, XL

Buy a call option at a Higher Strike Price, XH.

Sell two call options at an intermediate Strike Price XM


The investor thinks that there will be no large stock price movements.

That is, the investor believes that markets are not volatile

This strategy will lead him to a profit if the stock price stays close to XM,

but will give him a small limited loss if there is a significant stock pricemovement in the either direction

Equation:

Profit = max (SXL , 0)CL + max (SXH , 0)CH2 [max (SXM), 0] + 2 CM

B fl S d i


71/85

Butterfly Spreads using

Put Options

Construction:

Buy a put option at a Lower Strike Price, XL

Buy a put option at a Higher Strike Price, XH.

Sell two call options at an intermediate Strike Price XM




This strategy will lead him to a profit if the stock price stays close to XM,

but will give him a small limited loss if there is a significant stock pricemovement in the either direction

Equation:

Profit = max (XL-S , 0)PL + max (XH - S, 0)PH2 [max (XM - S), 0] + 2 PM

C l d S d i


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Calendar Spreads using

2 Call Options

Construction:

Sell a call option at X

Buy a call option at X with longer maturity




This strategy will lead him to a profit if the stock price stays close to X, but

will give him a small limited loss if there is a significant stock price

movement in the either direction The longer the maturity of an option, the more expensive it actually is. The

calendar spread requires an initial investment

Profits are usually produced when the short maturity option expires on the

assumption that the long maturity option is sold at that time

C l d S d i


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Calendar Spreads using

2 Put Options

Construction:

Sell a put option at X

Buy a put option at X with longer maturity




This strategy will lead him to a profit if the stock price stays close to X, but

will give him a small limited loss if there is a significant stock price

movement in the either direction The longer the maturity of an option, the more expensive it actually is. The

calendar spread requires an initial investment

Profits are usually produced when the short maturity option expires on the

assumption that the long maturity option is sold at that time


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Long Straddle

Construction:

Buy a call option at a Strike Price X

Buy a put option at a Strike Price X.

Whats in the Investors mind? The investor thinks that there will be large stock price movements but is

not sure of in which direction will the prices move.

That is, the investor believes that markets would be volatile

This strategy will lead him to a profit if there is a significant stock price

movement in the either direction This strategy will lead him to a loss if the stock price remains equal to or

close to the strike price at expiration

Equation:

Profit = max (S - X , 0)C + max (X - S, 0)P


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Short Straddle

Construction:

Sell a call option at a Strike Price X

Sell a put option at a Strike Price X.


The investor thinks that there will be no large stock price movements

That is, the investor believes that markets would not be volatile

This strategy will lead him to a profit if there is no significant stock price

movement in the either direction

This strategy will lead him to a loss if the stock price moves significantly tothe strike price at expiration

Equation:

Profit = -max (S - X , 0) + C - max (X - S, 0) + P

L St l


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Long StrangleConstruction: Buy a call option at a relatively Higher Strike Price XH

Buy a put option at a relatively Lower Strike Price XL

Whats in the Investors mind? A Strangle is similar to a Straddle except that the option purchased is slightly out

of the money. Therefore it is cheaper to implement than the Straddle.

The investor thinks that there will be large stock price movements but is not sure

of in which direction will the prices move. That is, the investor believes that markets would be volatile

This strategy will lead him to a profit if there is a significant stock pricemovement in the either direction

This strategy will lead him to a loss if the stock price remains equal to or close tothe strike price at expiration

Because Strangles are Cheaper, the stock will have to move more relative to thestraddle before the strangle pay offs.

Equation:

Profit = max (S - XL , 0)C + max (XH - S, 0)P

Sh t St l


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Short StrangleConstruction: Buy a call option at a relatively Higher Strike Price XH

Buy a put option at a relatively Lower Strike Price XL

Whats in the Investors mind? A Strangle is similar to a Straddle except that the option purchased is slightly out

of the money. Therefore it is cheaper to implement than the Straddle.

The investor thinks that there will be no large stock price movements

That is, the investor believes that markets would not be volatile This strategy will lead him to a profit if there is no significant stock price

movement in the either direction

This strategy will lead him to a loss if the stock price moves significantly to thestrike price at expiration

Because Strangles are Cheaper, the stock will have to move more relative to the

straddle before the strangle pay offs.

Equation:

Profit = - max (S - XL , 0) + C - max (XH - S, 0) + P


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Strips

Construction:

Buy 2 put options at a Strike Price X

Buy 1 call option at a Strike Price X.


The investor believes that there will be large stock price movements but

also thinks that the probability of the significant downward movement is

higher than the upward movement.

The investor believes that markets would be volatile

That is a strip is betting on volatility but is more bearish since it pays offmore on the downside

Equation:

Profit = max (S - X , 0)C + 2 [max (X - S, 0)]2P


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Straps

Construction:

Buy 2 call options at a Strike Price X

Buy 1 put option at a Strike Price X.


The investor believes that there will be large stock price movements but

also thinks that the probability of the significant upward movement is

higher than the downward movement.

The investor believes that markets would be volatile

That is a strap is betting on volatility but is more bullish since it pays offmore on the upside

Equation:

Profit = 2[max (S - X , 0)]2C + [max (X - S, 0)]P


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Concept Checkers

Which of the following is the riskiest form of speculation usingoption contracts ?

a) Setting up a spread using call options

b) Buying put options

c) Writing naked call options

d) Writing naked put options

Which of the following will create a bull spread ?

a) Buy a put with a strike price of X = 50 , and sell a put with K = 55 .

b) Buy a put with a strike price of X = 55 , and sell a put with K = 50c) Buy a call with a premium of 5, and sell a call with a premium of 7

d) Buy a call with a strike price of X = 50 , and sell a put with K = 55


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Which of the following regarding option strategies is/are notcorrect ?1. A long strangle involves buying a call and a put with equal strike prices

2. A short bull spread involves selling a call at lower strike price andbuying another call at higher strike price.

3. Vertical spreads are formed by options with different maturities .

4. Along butterfly spread is formed by buying 2 options at two differentstrike prices and selling another 2 options at the same strike price .

1 only

1 & 3 only

1 &2 only

3 &4 only

Concept Checkers


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Concept Checkers

What is a lower bound for the price of a 4 month call option on a non-dividendpaying stock when the stock price is $28, the strike price is $25, and the risk freeinterest rate is 8% per annum ?

What is a lower bound for the price of a 1 month European put option on a non-dividend paying stock when the stock price is $12, the strike price is $15, and therisk free interest rate is 6% per annum ?

What is a lower bound for the price of a 6 month call option on a non-dividendpaying stock when the stock price is $80, the strike price is $75, and the risk freeinterest rate is 10% per annum ?


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Concept Checkers

An investor purchases a call on a stock, with an exerciseprice of $42 and a premium of $ 1.50 , and purchases a putoption with the same maturity that has an exercise price of$45 and a premium of $2. Compute the payoff of a stranglestrategy if the stock is at $40.

An investor sells a put for PL0=#3.00 with a strike of X=$20and purchases a put for PH0=$4.5 with a strike price of $40.Compute the payoff of a bear put spread strategy when the

price of the stock is at $35.


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Thank You!

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MMS Derivatives Lec 1