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Options Markets:Options Markets:IntroductionIntroduction

Chapter 20Chapter 20

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Buy - Long Sell - Short Call Put Key Elements

- Exercise or Strike Price

- Premium or Price

- Maturity or Expiration

Option TerminologyOption Terminology

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In the Money - exercise of the option would be profitable

Call: market price>exercise price

Put: exercise price>market price

Out of the Money - exercise of the option would not be profitable

Call: market price>exercise price

Put: exercise price>market price

At the Money - exercise price and asset price are equal

Market and Market and Exercise Price RelationshipsExercise Price Relationships

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American - the option can be exercised at any time before expiration or maturity

European - the option can only be exercised on the expiration or maturity date

American vs European OptionsAmerican vs European Options

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Stock Options Index Options Futures Options Foreign Currency Options Interest Rate Options

Different Types of OptionsDifferent Types of Options

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Notation

Stock Price = ST Exercise Price = X

Payoff to Call Holder

(ST - X) if ST >X

0 if ST < X

Profit to Call Holder

Payoff - Purchase Price

Payoffs and Profits on Options at Payoffs and Profits on Options at Expiration - CallsExpiration - Calls

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Payoff to Call Writer

- (ST - X) if ST >X

0 if ST < X

Profit to Call Writer

Payoff + Premium

Payoffs and Profits on Options at Payoffs and Profits on Options at Expiration - CallsExpiration - Calls

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Payoff Profiles for CallsPayoff Profiles for CallsPayoff

Stock Price

0

Call Writer

Call Holder

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Payoffs to Put Holder

0 if ST > X

(X - ST) if ST < X

Profit to Put Holder

Payoff - Premium

Payoffs and Profits at Payoffs and Profits at Expiration - PutsExpiration - Puts

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Payoffs to Put Writer

0 if ST > X

-(X - ST) if ST < X

Profits to Put Writer

Payoff + Premium

Payoffs and Profits at Payoffs and Profits at Expiration - PutsExpiration - Puts

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Payoff Profiles for PutsPayoff Profiles for Puts

0

Payoffs

Stock Price

Put Writer

Put Holder

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Investment Strategy Investment

Equity only Buy stock @ 100 300 shares $10,000

Options only Buy calls @ 10 1000 options $10,000

Leveraged Buy calls @ 10 100 options $1,000equity Buy T-bills @ 2% $9,000

Yield

Equity, Options & Equity, Options & Leveraged Equity - Text ExampleLeveraged Equity - Text Example

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IBM Stock Price

$95 $105 $115

All Stock $9,500 $10,500 $11,500

All Options $0 $5,000 $15,000

Lev Equity $9,270 $9,770 $10,770

Equity, Options & Equity, Options & Leveraged Equity - PayoffsLeveraged Equity - Payoffs

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IBM Stock Price

$95 $105 $115

All Stock -5.0% 5.0% 15%

All Options -100% -50% 50%

Lev Equity -7.3% -2.3% 7.7%

Equity, Options & Equity, Options & Leveraged Equity - Rates of ReturnLeveraged Equity - Rates of Return

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Protective PutProtective Put

Use - limit loss

Position - long the stock and long the put

Payoff ST < X ST > X

Stock ST ST

Put X - ST 0

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Protective Put ProfitProtective Put Profit

ST

Profit

-P

Stock

Protective Put Portfolio

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Covered CallCovered Call

Use - Some downside protection at the expense of giving up gain potential

Position - Own the stock and write a call

Payoff ST < X ST > X

Stock ST ST

Call 0 - ( ST - X)

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Covered Call ProfitCovered Call Profit

ST

Profit

-P

Stock

Covered Call Portfolio

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Straddle (Same Exercise Price)

Long Call and Long Put

Spreads - A combination of two or more call options or put options on the same asset with differing exercise prices or times to expiration

Vertical or money spread

Same maturity

Different exercise price

Horizontal or time spread

Different maturity dates

Option StrategiesOption Strategies

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ST < X ST > X

Payoff for

Call Owned 0 ST - X

Payoff for

Put Written-( X -ST) 0

Total Payoff ST - X ST - X

Put-Call Parity RelationshipPut-Call Parity Relationship

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Long Call

Short Put

Payoff

Stock Price

Combined =Leveraged Equity

Payoff of Long Call & Short PutPayoff of Long Call & Short Put

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Since the payoff on a combination of a long call and a short put are equivalent to leveraged equity, the prices must be equal.

C - P = S0 - X / (1 + rf)T

If the prices are not equal arbitrage will be possible

Arbitrage & Put Call ParityArbitrage & Put Call Parity

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Stock Price = 110 Call Price = 17

Put Price = 5 Risk Free = 10.25%

Maturity = .5 yr X = 105

C - P > S0 - X / (1 + rf)T

17- 5 > 110 - (105/1.05)

12 > 10

Since the leveraged equity is less expensive, acquire the low cost alternative and sell the high cost alternative

Put Call Parity - Put Call Parity - Disequilibrium ExampleDisequilibrium Example

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Put-Call Parity ArbitragePut-Call Parity Arbitrage

Immediate Cashflow in Six MonthsPosition Cashflow ST<105 ST> 105

Buy Stock -110 ST ST

BorrowX/(1+r)T = 100 +100 -105 -105

Sell Call +17 0 -(ST-105)

Buy Put -5 105-ST 0

Total 2 0 0

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Optionlike SecuritiesOptionlike Securities

Callable Bonds Convertible Securities Warrants Collateralized Loans

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Exotic OptionsExotic Options

Asian Options Barrier Options Lookback Options Currency Translated Options Binary Options