Introduction

• A derivative is a financial instrument whose return is derived from the return on another instrument.

• Size of the derivatives market at year-end 2001: $3.8 trillion in market value

• All financial institutions can make some productive use of derivative assets

• Use of Derivatives:

– Risk Management—Hedging and tuning risk to an acceptable level

– Speculation and tactical asset allocation—Maximize thrust in a given asset class

– Of course, arbitrage operations from temporally mispriced securities

– Operational Advantages: Low transaction costs, very liquid, can be written (short-sold) easily

Categories of Derivatives

FuturesListed, OTC futuresForward contracts

OptionsCallsPuts

SwapsInterest rate swapForeign currency swap

Derivatives

Options• Option terminology

• price/premium• call/put• exchange-listed; over-the-counter options

• An option is the right to either buy or sell something at a set price, within a set period of time– The right to buy is a call option– The right to sell is a put option

• You can exercise an option if you wish, but you do not have to do so

Futures Contracts• Futures contracts involve a promise to exchange a product for cash

by a set delivery date. So, futures contracts deal with transactions that will be made in the future.

• A futures contract involves a process known as marking to market– Money actually moves between accounts each day as prices move

up and down• A forward contract is functionally similar to a futures contract,

however:– There is no marking to market– Forward contracts are not marketable– Exclusively over-the-counter

Swaps• Swaps are arrangements in which one party trades something

with another party—i.e. cash flows• The swap market is very large, with trillions of dollars

outstanding• In an interest rate swap, one firm pays a fixed interest rate on a

sum of money and receives from some other firm a floating interest rate on the same sum– Popular with corporate treasurers as risk management tools

and as a convenient means of lowering corporate borrowing costs

• In a foreign currency swap, two firms initially trade one currency for another

• Subsequently, the two firms exchange interest payments, one based on a foreign interest rate and the other based on a U.S. interest rate. Finally, the two firms re-exchange the two currencies

Product Characteristics• Both options and futures contracts exist on a wide variety of

assets– Options trade on individual stocks, on market indexes, on

metals, interest rates, or on futures contracts– Futures contracts trade on products such as wheat, live cattle,

gold, heating oil, foreign currency, U.S. Treasury bonds, and stock market indexes

• The underlying asset is that which you have the right to buy or sell (with options) or the obligation to buy or deliver (with futures)

• Listed derivatives trade on an organized exchange such as the Chicago Board Options Exchange or the Chicago Board of Trade

• OTC derivatives are customized products that trade off the exchange and are individually negotiated between two parties

• Options are securities and are regulated by the Securities and Exchange Commission (SEC)

• Futures contracts are regulated by the Commodity Futures Trading Commission (CFTC)

Derivative Usage • Hedging: If someone bears an economic

risk and uses the futures market to reduce that risk, the person is a hedger

• Speculating: A person or firm who accepts the risk the hedger does not want to take is a speculator. Speculators believe the potential return outweighs the risk

– The primary purpose of derivatives markets is not speculation. Rather, they permit the transfer of risk between market participants as they desire

• Arbitrage is the existence of a riskless profit. Arbitrage opportunities are quickly exploited and eliminated. Persons actively engaged in seeking out minor pricing discrepancies are called arbitrageurs. Arbitrageurs keep prices in the marketplace efficient

Hedgers SpeculatorsRisk Transfer

Application of Derivatives• Risk management:The hedger’s primary motivation is risk

management– Someone who is bullish believes prices are going to rise. Someone who is

bearish believes prices are going to fall. Then, we can tailor our risk exposure to any points we wish along a bullish/bearish continuum

• Income generation: Writing an option is a way to generate income. It involves giving someone the right to purchase or sell your stock at a set price in exchange for an up-front fee (the option premium) that is yours to keep no matter what happens. Popular during a flat period in the market or when prices are trending downward

• Financial engineering refers to the practice of using derivatives as building blocks in the creation of some specialized product. Financial engineers:Select from a wide array of puts, calls futures, and other derivatives and know that derivatives are neutral products (neither inherently risky nor safe)

OPTIONS

Options Basics• A call option gives its owner the right to buy; it is not a promise to

buy. A put option gives its owner the right to sell; it is not a promise to sell.

• An American option gives its owner the right to exercise the option anytime prior to option expiration. A European option may only be exercised at expiration– Options giving the right to buy or sell shares of stock (stock

options) are the best-known options. An option contract is for 100 shares of stock

– The underlying asset of an index option is some market measure like the S&P 500 index.It is Cash-settled

• Option characteristics• Expiration dates:The Saturday following the third Friday of

certain designated months for most options• Striking price: The predetermined transaction price, in multiples

of $2.50 or $5, depending on current stock price• Underlying Security: The security the option gives you the right to

buy or sell. Both puts and calls are based on 100 shares of the underlying security

Opening and Closing Transactions• The first trade someone makes in a particular option is an opening transaction• When the individual subsequently closes that position out with a second trade,

this latter trade is a closing transaction• When someone buys an option as an opening transaction, the owner of an

option will ultimately do one of three things with it:– Sell it to someone else– Let it expire– Exercise it:1)Notify your broker; 2) Broker notifies the Options Clearing

Corporation who selects a contra party to receive the exercise notice• The option premium is not a down payment on the purchase of the stock• The option holder, not the option writer, decides when and if to exercise• In general, you should not buy an option with the intent of exercising it

• When someone sells an option as an opening transaction, this is called writing the option– No matter what the owner of an option does, the writer of the option keeps

the option premium that he or she received when it was sold

The Role of the Options Clearing Corporation (OCC)

• The Options Clearing Corporation (OCC) contributes substantially to the smooth operation of the options market– It positions itself between every buyer and seller and

acts as a guarantor of all option trades– It sets minimum capital requirements and provides

for the efficient transfer of funds among members as gains or losses occur

Exchanges• Major options exchanges in the

U.S.:– Chicago Board Options

Exchange (CBOE)– American Stock Exchange

(AMEX)– Philadelphia Stock Exchange

(Philly)– Pacific Stock Exchange (PSE)– International Securities

Exchange (ISE)• Bid Price and Ask Price• Types of orders

– A market order and limit order ( specifies a particular price (or better) beyond which no trade is desired. It requires a time limit, such as “for the day” or “good ‘til canceled (GTC)”

• Margins

MAY 2005

CallsLastSale

NetChg

Bid Ask VolOpenInterest

Puts

MAY 2005 20 IYZET

$3.60 unch $3.20 $3.60 N.A. N.A.MAY 2005 20 IYZQT

MAY 2005 21 IYZEU

$0.85 unch $0.05 $0.15 N.A. 73MAY 2005 21 IYZQU

MAY 2005 22 IYZEV

$0.05 unch $0.05 $0.05 13 2,200MAY 2005 22 IYZQV

MAY 2005 23 IYZEW

$1.50 unch $0.90 $1.15 N.A. 52MAY 2005 23 IYZQW

MAY 2005 24 IYZEX

$1.45 unch $0.40 $0.65 N.A. 15MAY 2005 24 IYZQX

MAY 2005 25 IYZEY

$0.35 unch $0.15 $0.40 N.A. 4MAY 2005 25 IYZQY

MAY 2005 26 IYZEZ

$1.00 unch $0.00 $0.25 N.A. 2MAY 2005 26 IYZQZ

Underlying Symbol Last Sale Net Change

iShares Dow Jones US Telecommunications IYZ 23.15 0.2000   

Option Terminology

• Option= right to buy or sell an asset at a fixed price and by a specific time.

• Call Option= right to buy the underlying asset.• Put Option=the right to sell the underlying asset.• Exercise Price (Strike Price or X): Fixed price at

which the underlying asset can be bought or sold.• Option Premium (C=call; P=put): Price of the

option itself.

The Option Premium =Intrinsic Value + Time Value

• Intrinsic value is the amount that an option is immediately worth given the relation between the option striking price and the current stock price

• For a call option, intrinsic value =MAX(0,stock price –striking price)• For a put option, intrinsic value =MAX(0,striking price – stock price)

– Intrinsic value cannot be < zero• Out, at and in-the -money

– An option with no intrinsic value is out-of-the-money– An option whose striking price is exactly equal to the price of the

underlying security is at-the-money– Options that are “almost” at-the-money are near-the-money– An option whose striking price is positive is in-the-money

• Time value is equal to the premium minus the intrinsic value– As an option moves closer to expiration, its time value decreases (time value

decay)– AKA: speculative value

• Difference between option premium and intrinsic value.

– Speculative value=0 at maturity

– Before, speculative value= the chance that the option will expire in-the-money; e.g., the intrinsic value is greater than zero!

Intrinsic Value of Option • Value if option is exercised immediately= Intrinsic

value:– Call option: MAX(0,S-X)

– Put option: MAX(0,X-S)

• In-the-money:– Call: S>X

– Put: X>S

• Out-of-the-money: – Call: S<X

– Put: X<S

• At-the-money: X=S

Illustration :Assume that you bought a call option 3 months ago at $10 with a strike at $100

Stock price at maturity

ST

Initial premium (negative cash

flow) -Co

STRIKE X

Out, At, In-the money

Intrinsic value= C=

MAX(S-X,0)

BALANCE or PAYOFF -Co+ C

60 -10 100 OUT MAX(60-100,0)=0 -10 70 -10 100 OUT 0 -10 80 -10 100 OUT 0 -10 90 -10 100 OUT 0 -10

100 -10 100 AT 0 -10 110 -10 100 IN 10 0 120 -10 100 IN 20 10 130 -10 100 IN 30 20 140 -10 100 IN 40 30

Illustration 2: Assume that you sold a call option 3 months ago at $10 with a strike at $100

Stock price atmaturity

ST

Initial premium (positive cash

flow) Co

STRIKE X

Out, At, In-themoney

Intrinsic value= -C=

-MAX(S-X,0)

BALANCE orPAYOFF

Co-C

60 10 100 OUT -MAX(60-100,0)=0 10 70 10 100 OUT 0 10 80 10 100 OUT 0 10 90 10 100 OUT 0 10 100 10 100 AT 0 10 110 10 100 IN -10 0 120 10 100 IN -20 -10 130 10 100 IN -30 -20 140 10 100 IN -40 -30

Expiration Date Payoffs to Long and Short Call Positions

Illustration 3: Assume that you bought a put option 3 months ago at $10 with a strike at $100

Stock price atmaturity

ST

Initial premium (negative cash

flow) -Po

STRIKE X

Out, At, In-themoney

Intrinsic value= P=

MAX(X-S,0)

BALANCE orPAYOFF -Po+ P

60 -10 100 IN MAX(100-60,0)=40 30 70 -10 100 IN 30 20 80 -10 100 IN 20 10 90 -10 100 IN 10 0 100 -10 100 AT 0 -10 110 -10 100 OUT 0 -10 120 -10 100 OUT 0 -10 130 -10 100 OUT 0 -10 140 -10 100 OUT 0 -10

Illustration 4: Assume that you sold a put option 3 months ago at $10 with a strike at $100

Stock price atmaturity

ST

Initial premium (positive cash

flow) Po

STRIKE X

Out, At, In-themoney

Intrinsic value= -P=

-MAX(X-S,0)

BALANCE orPAYOFF

Po-P

60 10 100 IN -MAX(100-60,0)= -40 -30 70 10 100 IN -30 -20 80 10 100 IN -20 -10 90 10 100 IN -10 0 100 10 100 AT 0 10 110 10 100 OUT 0 10 120 10 100 OUT 0 10 130 10 100 OUT 0 10 140 10 100 OUT 0 10

Expiration Date Payoffs to Long and Short Put Positions

Portfolio Risk Management• Rational

• How:

• Narrowing the distribution– Diversification between classes– Beta positioning

• “Skewing” the distribution to the left with Options– Covered call– Escrowed puts– 90/10– Protective puts

Put-Call-Spot Parity

Put-Call-Spot Parity

S + P - C = X(1 + Rf)-T

• where:

Rf = the annualized risk-free rate

T = the time to maturity in years

Let X(1 + Rf)-T = the proceed of a T-bill with a face value of X

Then(long stock) + (long put) - (short call) = (long T-bill)

Put-Call-Spot Parity

Creating Synthetic SecuritiesUsing Put-Call Parity

T-bill=S + P - C

Put= X(1 + Rf)-T - S + C

Call = S + P - X(1 + Rf)-T

Stock = X(1 + Rf)-T - P + C

Questions• How can the put-call parity be used in the risk

management framework?

• Determine the “payoff” of a position that consists of a long position in a put and a futures contract and a short position in a call (same exercise and maturity for the options; same underlying asset for the futures)

• How can you use this information for risk management purpose?

Combinations of Options• Hedging:

–Protective put–Covered call–Covering a Short position

Protecting Portfolio Value with Put Options• Protective puts

– Hedges downside losses– Protective put=S+P=C+T-bill

• Example:– Portfolio value = $100 million– 3-month put quote on Nasdaq100=52.96 (spot=4000,

strike=4000)– 1 Nasdaq contract is based on a price of $400,000 (index

price x 100=$400,000); the premium costs $5,296 for 1 contract(100 x 52.6)

– you need 250 contracts ($ to hedge/$ of 1 contract = 100M/0.4M)

– 3-month put premium 1.324 million (250 x 52.96 X100)

Expiration Date Value of a Protective Put Position

Portfolio valueIn million$

PoIn million$

XIn million$

PIn million$

PayoffPortfolio value+P-Po

60 1.324 100 40 98.67670 1.324 100 30 98.67680 1.324 100 20 98.67690 1.324 100 10 98.676100 1.324 100 0 98.676110 1.324 100 0 108.676120 1.324 100 0 118.676130 1.324 100 0 128.676140 1.324 100 0 138.676

0

50

100

150

Portfolio value

Payoff

Portfolio value 60 70 80 90 100 110 120 130 140

Payoff 98.7 98.7 98.7 98.7 98.7 109 119 129 139

1 2 3 4 5 6 7 8 9

Simulated Portfolio Return Distributions

Questions• What would happen to our “protected” position, if

we bought:

• OTM puts?

• ITM puts?

Another Example: Protective PutRATIONAL: Investors may anticipate a decline in the value of an Investment but cannot conveniently sell.OPERATION: LONG PUT & LONG STOCK INITIALLY, -So-Po AT MATURITY: S(T)+MAX(X-S(T),0) PROFIT (AT MATURITY)=

S(T)+MAX(X-S(T),0)-So-PoEXAMPLE: purchased Microsoft for $28.51 and a

Microsoft APR 25 put for $1.10 BREAKEVEN: IF S(T)<X, S(T)+X-S(T)-So-Po=0 NO

SOLUTIONS FOR S(T)IF S(T)>X, S(T)-So-

Po=0S(T)=So+Po=28.51+1.1=29.61IN SUM:-The maximum loss is $4.61-The maximum loss occurs at all stock prices

of $25 or below-The put breaks even somewhere between

$25 and $30 (it is exactly $29.61)-The maximum gain is unlimited

S(T)Stock Price at Option Expiration

0 5 15 25 30 40

S(T)-So -28.51 -23.51 -13.51 -3.51 1.49 11.49

MAX(X-S(T),0)-Co

23.90 18.90 8.90 -1.10 -1.10 -1.10

PROFIT -4.61 -4.61 -4.61 -4.61 0.39 10.39

Stock price at option expiration

0

4.61

25

29.61

Logic Behind the Protective Put• A protective put is like an insurance policy

– You can choose how much protection you want

• The put premium is what you pay to make large losses impossible– The striking price puts a lower limit on your

maximum possible lossLike the deductible in car insurance

– The more protection you want, the higher the premium you are going to pay

• A protective put is an example of a synthetic call

Altering Portfolio Payoffs with Call Options

• Covered calls– Call writer owns the stock: S-C=T-bill - P

• Benefits– If you wish, the cash received from the sell of the calls

shifts the downside potential up; this is a dangerous strategy that may be used to profit in a “neutral-bearish” and low volatility market

• Danger– Prices could fall very very badly.

ExampleA fund manager writes covered calls against the $100 million

fund and receives the premium of $2.813 million,

The calls have been chosen so that the strike is 100 million (ATM)

if your portfolio follows the NASDAQ100, which is quoted at 4000, a 3-month “at-the money” option (strike is 4000) is priced at 112.52.

1 contract is 100 times the index, so a call with a strike at 4000 correspond to $400,000 and is priced at $11,252.

You need to cover $100,000,000; thus, you need 250 contracts (100m/0.4), which cost in total $2.813 M (11,252 x 250).

.

Altering Portfolio Payoffs with Call Options

Portfolio value(millions)

Co(millions)

X(millions)

C(millions)

PositionPortfolio value+Co-C

60 2.813 100 0 62.81370 2.813 100 0 72.81380 2.813 100 0 82.81390 2.813 100 0 92.813100 2.813 100 0 102.813110 2.813 100 10 102.813120 2.813 100 20 102.813130 2.813 100 30 102.813140 2.813 100 40 102.813

0

20

40

60

80

100

120

140

160

Portfolio value

Position

Portfolio value 60 70 80 90 100 110 120130 140

Position 63 73 83 93 103 103 103103 103

1 2 3 4 5 6 7 8 9

Questions• What are the advantages of a covered call strategy?

• Under what circumstance(s) would you use a covered call strategy Vs. a protective put strategy?

• Your portfolio is not traded in the option market; only index options are traded. How would set the number of puts to buy or calls to sell in practice?

HEDGING: Covered Calls• Rational: Useful for investors anticipating a drop in the market but unwilling

to sell the shares now • Operation: Long stock and short callInitially: -So+CoAt maturity: S(T)-Max(S(T)-X,0)Profit at maturity: -So+Co+S(T)-Max(S(T)-X,0)• Example: Write a JAN 30 covered call on Microsoft @ $1.20; buy stock @

28.51 • Break-even: -So+Co+S(T)-Max(S(T)-X,0)=0If S<X, -So+Co+S(T)=0S(T)=So-C0=28.51-1.20=27.31If S>X, -So+Co+S(T)-S(T)+X=0No solution• In sum: The call premium cushions the loss. This is a synthetic short put.

Stock price at option expiration

0

27.31

30

2.69

27.31

HEDGING: Covering a short position• Rational: Call options can be used to

provide a hedge against losses resulting from rising security pricesThe potential for unlimited losses is eliminated

• Operation: Short stock and long callInitially: So-CoAt maturity: -S(T)+Max(S(T)-X,0)Profit at maturity: So-Co -S(T)+Max(S(T)-

X,0)• Example: Assume you short sold

Microsoft for $28.51and purchased an APR 35 call at $0.50 in addition to the short sale

• Breakeven: So-Co -S(T)+Max(S(T)-X,0)=0

If S<X, So-Co -S(T)=0S(T)=So-Co=28.51-0.5=28.01

If S>X, So-Co -S(T)+S(T)-X=0No Solution

• In sum: This is a synthetic put; Many investors

prefer the put – The loss is limited to the option premium– Buying a put requires less capital than

margin requirements

Stock Price at Option Expiration

-6.99-6.99-0.503.0113.0128.01Net

4.50-0.50-0.50-0.50-0.50-0.50Long 35 call

@ $0.50

-11.49-6.4903.5113.5128.51Short stock

@ $28.51

403528.5125150

Stock Price at Option Expiration

-6.99-6.99-0.503.0113.0128.01Net

4.50-0.50-0.50-0.50-0.50-0.50Long 35 call

@ $0.50

-11.49-6.4903.5113.5128.51Short stock

@ $28.51

403528.5125150

Stock price at option expiration

0

6.99

35

28.01

28.01

The potential forunlimited loss is gone

Bottom-lineEscrowed puts - writing put options and investing in Treasury bills an amount

equal to the discounted strike price of the puts. (X-P)90/10 strategy- A method of investment in which one places approximately 90% of his funds in

risk-free, interest-bearing assets such as Treasury bills, and buys options with the remainder 10%.X+C

Bearish Neutral-Bearish Neutral Neutral-Bullish

Bullish

Protective put (ITM)

M Protective put

 

Protective put (ATM)

Covered call (ITM)

Protective put(OTM)90/10(ITM)

Escrowed puts(OTM)

Covered Call (ATM)

90/10(ATM)

Escrowed puts

(ATM) 

M 90/10(OTM)

M Escrowed

puts(ITM)

Why Options Are a Good Idea• Increased risk

• Instantaneous information

• Portfolio risk management

• Risk transfer

• Financial leverage

• Income generation

Generate income with options: Writing Calls• Attractive way to generate income with foundations, pension funds, and other

portfolios. Also, very popular activity with individual investors. Writing calls may not be appropriate when option premiums are very low (duh!) and the option is very long-term.

• Example of Covered calls: You bought 300 shares of Microsoft at $22. You write three JAN 30 calls @ $1.20, or $120.00 on 100 shares.

• Profit Equation: -So+Co+S(T)-Max(S(T)-X,0) • Breakeven: -So+Co+S(T)-Max(S(T)-X,0)=0 Solution when S(T)<X, that is

S(T)=So-Co=22-1.2=20.8• Observation: same as short putIf prices advance above the striking price of

$30, your stock will be called away and you must sell it to the owner of the call option for $30 per share, despite the current stock price. If Microsoft trades for $30, you will have made a good profit, since the stock price has risen substantially. Additionally, you retain the option premium.

• Writing Naked Calls are very risky due to the potential for unlimited losses• Example of naked calls: It is now September 15; a SEP 35 MSFT call exists

with a premium of $0.05; the SEP 35 MSFT call expires on September 19; Microsoft currently trades at $28.51.A brokerage firm feels it is extremely unlikely that MSFT stock will rise to $35 per share in ten days. The firm decides to write 100 SEP 35 calls. The firm receives $0.05 x 10,000 = $500 now. If the stock price stays below $35, nothing else happens. If the stock were to rise dramatically, the firm could sustain a large loss.

• Profit Equation:Co-Max(S(T)-X,0) • Breakeven: Co-Max(S(T)-X,0)=0, when S(T)>X,S(T)=X+Co=35+0.05=35.05

Generate income with Puts• A naked put means a short put by itself. A covered put means the

combination of a short put and a short stock positionA short stock position would cushion losses from a short put: Short stock + short put ≈ short call

• Put overwriting involves owning shares of stock and simultaneously writing put options against these shares.– Both positions are bullish – Appropriate for a portfolio manager who needs to generate

additional income but does not want to write calls for fear of opportunity losses in a bull market

• Example: investor simultaneously buys shares of MSFT at $28.51 and writes an OCT 30 MSFT put for $2

Stock Price at Option Expiration

0 15 25 28.255

30 35

Buy stock

@ $28.51

-28.51 -13.51 -3.51 -0.255 1.49 6.49

Write 30 put

@ $2

-28.00 -13.00 -3.00 0.255 2.00 2.00

Net -56.51 -26.51 -6.51 0.00 3.49 8.49

Stock price at option expiration

0

56.51

30

3.49

Breakeven point = 28.255

Adding A Put to an Existing Stock Position

Stock Price at Option Expiration

0 10 25 30 35 40

Long stock @ $22 -22 -12 +3 +8 +13 +18

Long 25 put @ $1.10 +23.90 +13.90 -1.10 -1.10 -1.10 -1.10

Net 1.90 1.90 1.90 6.90 11.90 16.90

•Assume an investor: Bought MSFT @ $22 and Buys an APR 25 MSFT put @ $1.10;The stock price is currently $28.51

Stock price at option expiration

025

1.90

Writing A Call Against an Existing Stock Position

Stock price at option expiration

0

20.80

30

9.20

20.80

•Assume an investor Bought MSFT @ $22 and Writes a JAN 30 call @ $1.20;The stock price is currently $28.51

Writing Calls to Improve on the Market

Writing Deep-in-the-Money Microsoft Calls ExampleAssume an institution holds 10,000 shares of MSFT. The current

market price is $28.51. OCT 20 call options are available @ $8.62. The institution could sell the stock outright for a total of $285,100. Alternatively, the portfolio manager could write 100 OCT 20 calls on MSFT, resulting in total premium of $86,200. If the calls are exercised on expiration Friday, the institution would have to sell MSFT stock for a total of $200,000. Thus, the total received by writing the calls is $286,200, $1,100 more than selling the stock outright.

Though, there is risk associated with writing deep-in-the-money calls– It is possible that Microsoft could fall deep below the striking price– It may not be possible to actually trade the options listed

Writing calls to improve on the marketInvestors owning stock may be able to increase the amount they receive from the sale of their stock by writing deep-in-the-money calls against their stock position

Writing Puts to Improve on the Market

• Writing puts to improve on the market– An institution could write deep-in-the-money puts

when it wishes to buy stock to reduce the purchase price

Speculating with options• Playing with expected volatility and

expected changes in market conditions.

  LONG SHORT

STRADDLE (Same X,M)

C+P -C-P

STRANGLE (≠ X, same M)

C(ITM)+P(OTM) -C(ITM)-P(OTM)

STRAP (Same X,M)

2C+P -C-2P

SPREAD(≠ X, same M)

C(ITM)-P(OTM) P(ITM)-C(OTM)

C-BUTTERFLY(≠ X, same M)

C(OTM)-2C(ATM)+C(ITM)

-C(OTM)+2C(ATM)-C(ITM)

Sample of quoted options with 6 months maturity

Hypothetical Stock andOption Prices

Instrument Exercise Price Market Price Intrinsic Value TimePreference

SAS Stock — $40.00 — —Call: #1 $35.00 8.07 $5.00 $3.07

#2 40.00 5.24 0.00 5.24#3 45.00 3.24 0.00 3.24

Put: #1 35.00 1.70 0.00 1.70#2 40.00 3.67 0.00 3.67#3 45.00 6.47 5.00 1.47

Terminal payoff for Long straddle (C+P) and short straddle (-C-P): same maturity and strike price (call 2

and Put 2)

S Co Po X C PPayoff Long Straddle

C+P-Co-PoPayoff Short Straddle

Co+Po-C-P20 5.24 3.67 40 0 20 11.09 -11.0925 5.24 3.67 40 0 15 6.09 -6.0930 5.24 3.67 40 0 10 1.09 -1.0935 5.24 3.67 40 0 5 -3.91 3.9140 5.24 3.67 40 0 0 -8.91 8.9145 5.24 3.67 40 5 0 -3.91 3.9150 5.24 3.67 40 10 0 1.09 -1.0955 5.24 3.67 40 15 0 6.09 -6.0960 5.24 3.67 40 20 0 11.09 -11.09

-20

0

20

40

60

80

S

Payoff LongStraddlePayoff ShortStraddle

S 20 25 30 35 40 45 50 55 60

Payof f LongStraddle

11.09 6.09 1.09 -3.91 -8.91 -3.91 1.09 6.09 11.09

Payof f ShortStraddle

-11.1 -6.09 -1.09 3.91 8.91 3.91 -1.09 -6.09 -11.1

1 2 3 4 5 6 7 8 9

Buying a Straddle: an other example • A long call is bullish; A long put is bearish• Why buy a long straddle?

– Whenever a situation exists when it is likely that a stock will move sharply one way or the other

• Suppose a speculator– Buys a JAN 30 call on MSFT @ $1.20– Buys a JAN 30 put on MSFT @ $2.75

• Equation: Max(S(T)-X,0)-Co+Max(X-S(T),0)-Po• Breakeven:Max(S(T)-X,0)-Co+Max(X-S(T),0)-Po=02 cases:(1) S<X, then -Co+X-S(T)-Po=0 S(T)=-Co+X-Po=-1.2+30-2.75=26.05(2) S>X, then S(T)-X-Co-Po=0 S(T)=X+Co+Po=30+1.2+2.75=33.95• The worst outcome for the straddle buyer is when both options expire

worthless. It occurs when the stock price is at-the-money. So the straddle buyer will lose money if stock closes near the striking price

Stock Price at Option Expiration

0 15 25 30 45 55

Long 30 call -1.20 -1.20 -1.20 -1.20 13.80 23.80

Long 30 put 27.25 12.25 2.25 -2.75 -2.75 -2.75

Net 26.05 11.05 -1.05 -3.95 11.05 21.05

Stock price at option expiration

0

3.95

30

26.05

26.05 33.95

Two breakeven points

Writing a Straddle

• The straddle writer wants little movement in the stock price. Losses are potentially unlimited on the upside because the short call is uncovered

Stock price at option expiration

0

26.05

30

3.95

26.05 33.95

Strangles• A strangle is similar to a

straddle, except the puts and calls have different striking prices.The speculator long a strangle expects a sharp price movement either up or down in the underlying security

• With a long strangle, the most popular version involves buying a put with a lower striking price than the call

• Suppose a speculator:– Buys a MSFT JAN 25 put @

$0.70

– Buys a MSFT JAN 30 call @ $1.20

Stock price at option expiration0

1.90

25

23.10

23.10 31.90

30

Writing a Strangle• The maximum gains for

the strangle writer occurs if both option expire worthless. It occurs in the price range between the two exercise prices.

Stock price at option expiration0

23.10

25

1.90

23.10 31.90

30

Condors• A condor is a less risky version

of the strangle, with four different striking prices

• The condor buyer hopes that stock prices remain in the range between the middle two striking prices

• Buyer:– Buys MSFT 25 calls @ $4.20– Writes MSFT 27.50 calls @ $2.40– Writes MSFT 30 puts @ $2.75– Buys MSFT 32.50 puts @ $4.60

• Seller:– writes MSFT 25 calls @ $4.20– buys MSFT 27.50 calls @ $2.40– buys MSFT 30 puts @ $2.75– writess MSFT 32.50 puts @ $4.60

Stock price at option expiration0

1.15

25

1.35

26.15

30

31.35

27.50 32.50

Stock price at option expiration0

1.15

25

1.35

26.15

30

31.35

27.50

32.50

Long Condor

Short Condor

Long Strap: 2 C + P (same maturity and strike)

ST Co Po X C=max(ST-X,0) P=max(X-ST,0)Payoff=

-2Co-Po+2C+P20 -5.24 -3.67 40 0 20 5.8525 -5.24 -3.67 40 0 15 0.8530 -5.24 -3.67 40 0 10 -4.1535 -5.24 -3.67 40 0 5 -9.1540 -5.24 -3.67 40 0 0 -14.1545 -5.24 -3.67 40 5 0 -4.1550 -5.24 -3.67 40 10 0 5.8555 -5.24 -3.67 40 15 0 15.8560 -5.24 -3.67 40 20 0 25.85

-20

0

20

40

60

80

S

Payoff

S 20 25 30 35 40 45 50 55 60

Payof f 5.85 0.85 -4.15 -9.15 -14.15 -4.15 5.85 15.85 25.85

1 2 3 4 5 6 7 8 9

Spreads• Option spreads are strategies in which the player

is simultaneously long and short options of the same type, but with different– Striking prices or possibly expiration dates

• In a vertical spread, options are selected vertically from the financial pages– The options have the same expiration date– The spreader will long one option and short the other

• Vertical spreads with calls– Bullspread– Bearspread

“Bull spread”: buy call no 1 (in-the money) and sell call no 3 (out-the money)

S C1o C3o X1 X2 C1 C3Payoff Bull SpreadC1-C3-C1o+C3o

20 8.07 3.24 35 45 0 0 -4.8325 8.07 3.24 35 45 0 0 -4.8330 8.07 3.24 35 45 0 0 -4.8335 8.07 3.24 35 45 0 0 -4.8340 8.07 3.24 35 45 5 0 0.1745 8.07 3.24 35 45 10 0 5.1750 8.07 3.24 35 45 15 5 5.1755 8.07 3.24 35 45 20 10 5.1760 8.07 3.24 35 45 25 15 5.17

-20

0

20

40

60

80

S

Payoff BullSpread

S 20 25 30 35 40 45 50 55 60

Payof f Bull Spread -4.8 -4.8 -4.8 -4.8 0.17 5.17 5.17 5.17 5.17

1 2 3 4 5 6 7 8 9

Comparing the Bull Money Spread and Long Call Positions

“Bear Spread”:buy put no 3 (in-the money) and sell put no l (out-the money).

S C1o C3o X1 X2 C1 C3Payoff Bull SpreadC1-C3-C1o+C3o

20 8.07 3.24 35 45 0 0 -4.8325 8.07 3.24 35 45 0 0 -4.8330 8.07 3.24 35 45 0 0 -4.8335 8.07 3.24 35 45 0 0 -4.8340 8.07 3.24 35 45 5 0 0.1745 8.07 3.24 35 45 10 0 5.1750 8.07 3.24 35 45 15 5 5.1755 8.07 3.24 35 45 20 10 5.1760 8.07 3.24 35 45 25 15 5.17

-20

0

20

40

60

80

S

Payoff BearSpread

S 20 25 30 35 40 45 50 55 60

Payoff BearSpread

5.235.23 5.23 5.230.23 -4.8 -4.8 -4.8 -4.8

1 2 3 4 5 6 7 8 9

Bullspread another example• Assume a person believes MSFT stock will appreciate

soonA possible strategy is to construct a vertical call bullspread :– Buy an APR 27.50 MSFT call

– Write an APR 32.50 MSFT call

• The spreader trades part of the profit potential for a reduced cost of the position.

• With all spreads the maximum gain and loss occur at the striking prices– It is not necessary to consider prices outside this range

– With a 27.50/32.50 spread, you only need to look at the stock prices from $27.50 to $32.50

Bullspread (cont’d)• Construct a profit and loss worksheet to form the

bullspread:

Stock Price at Option Expiration

0 27.50 28.50 30.50 32.50 50

Long 27.50 call @ $3

-3 -3 -2 0 2 19.50

Short 32.50 call @ $1

1 1 1 1 1 -16.50

Net -2 -2 -1 1 3 3

Stock price at option expiration0

2

3

32.50

29.50

27.50

Bearspread• A bearspread is the reverse of a bullspread

– The maximum profit occurs with falling prices– The investor buys the option with the lower striking

price and writes the option with the higher striking price

Vertical Spreads With Puts: Bullspread

• Involves using puts instead of calls. Buy the option with the lower striking price and write the option with the higher one

• The put spread results in a credit to the spreader’s account (credit spread)

• The call spread results in a debit to the spreader’s account (debit spread)

• A general characteristic of the call and put bullspreads is that the profit and loss payoffs for the two spreads are approximately the same– The maximum profit occurs at all stock prices above the higher striking

price– The maximum loss occurs at stock prices below the lower striking price

Calendar Spreads• In a calendar spread, options are chosen horizontally

from a given row in the financial pages– They have the same striking price– The spreader will long one option and short the other

• Calendar spreads are either bullspreads or bearspreads– In a bullspread, the spreader will buy a call with a distant

expiration and write a call that is near expiration– In a bearspread, the spreader will buy a call that is near

expiration and write a call with a distant expiration • Calendar spreaders are concerned with time decay

– Options are worth more the longer they have until expiration

Diagonal Spreads• A diagonal spread involves options from different

expiration months and with different striking prices– They are chosen diagonally from the option listing in

the financial pages

• Diagonal spreads can be bullish or bearish

Butterfly Spreads• A butterfly spread can be constructed for very

little cost beyond commissions

• A butterfly spread can be constructed using puts and calls

Stock price at option expiration0

Nonstandard Spreads: Ratio Spreads

• A ratio spread is a variation on bullspreads and bearspreads– Instead of “long one, short one,” ratio spreads involve

an unequal number of long and short options– E.g., a call bullspread is a call ratio spread if it

involves writing more than one call at a higher striking price

Nonstandard Spreads: Ratio Backspreads

• A ratio backspread is constructed the opposite of ratio spreads– Call bearspreads are transformed into call ratio

backspreads by adding to the long call position– Put bullspreads are transformed into put ratio

backspreads by adding more long puts

Nonstandard Spreads:Hedge Wrapper• A hedge wrapper involves writing a covered call and

buying a put– Useful if a stock you own has appreciated and is

expected to appreciate further with a temporary decline

– An alternative to selling the stock or creating a protective put

• The maximum profit occurs once the stock price rises to the striking price of the call

• The lowest return occurs if the stock falls to the striking price of the put or below

• The profitable stock position is transformed into a certain winner

• The potential for further gain is reduced

Combined Call Writing• In combined call writing, the investor writes calls

using more than one striking price

• An alternative to other covered call strategies

• The combined write is a compromise between income and potential for further price appreciation

Margin Considerations: • Necessity to post margin is an important consideration in

spreading: The speculator in short options must have sufficient equity in his or her brokerage account before the option positions can be assumed

• There is no requirement to advance any sum of money - other than the option premium and the commission required - to long calls or puts

• Can borrow up to 25% of the cost of the option position from a brokerage firm if the option has at least nine months until expiration

• For uncovered calls on common stock, the initial margin requirement is the greater of

Premium + 0.10(Stock Price)

• For uncovered puts on common stock, the initial margin requirement is 10% of the exercise price

Margin Requirements on Spreads• All spreads must be done in a margin account• More lenient than those for uncovered options• You must pay for the long side in full• You must deposit the amount by which the long put (or

short call) exercise price is below the short put (or long call) exercise price

• A general spread margin rule:– For a debit spread, deposit the net cost of the spread

– For a credit spread, deposit the different between the option striking prices

Margin Requirements on Covered Calls

• There is no margin requirement when writing covered calls

• Brokerage firms may restrict clients’ ability to sell shares of the underlying stock

Evaluating Spreads: Introduction

• Spreads and combinations are– Bullish,– Bearish, or– Neutral

• You must decide on your outlook for the market before deciding on a strategy

Evaluating Spreads: The Debit/Credit Issue

• An outlay requires a debit

• An inflow generates a credit

• There are several strategies that may serve a particular end, and some will involve a debt and others a credit

Evaluating Spreads: The Reward/Risk Ratio

• Examine the maximum gain relative to the maximum loss

• E.g., if a call bullspread has a maximum gain of $300.00 and a maximum loss of $200.00, the reward/risk ratio is 1.50

Evaluating Spreads: The “Movement to Loss” Issue

• The magnitude of stock price movement necessary for a position to become unprofitable can be used to evaluate spreads

Evaluating Spreads: Specify A Limit Price

• In spreads:– You want to obtain a high price for the options you

sell– You want to pay a low price for the options you buy

• Specify a dollar amount for the debit or credit at which you are willing to trade

Determining the Appropriate Strategy: Some Final Thoughts

• The basic steps involved in any decision making process:– Learn the fundamentals– Gather information– Evaluate alternatives– Make a decision