Options (Chapter 19 Jones)

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Options(Chapter 19 Jones)

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Potential Benefits of Derivatives

Derivative instruments: Value is determined by, or derived from, the value of another instrument vehicle, called the underlying asset or security

Risk shifting- Especially shifting the risk of asset price changes or interest rate changes to

another party willing to bear that risk Price formation

- Speculation opportunities when some investors may feel assets are mis-priced

Investment cost reduction- To hedge portfolio risks more efficiently and less costly than would

otherwise be possible

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Option characteristicsOptions are created by investors, sold to other investors Option to buy is a call option

Call options gives the holder the right, but not the obligation, to buy a given quantity of some asset at some time in the future, at prices agreed upon today.

Option to sell is a put optionPut options gives the holder the right, but not the obligation, to sell a given quantity of some asset at some time in the future, at prices agreed upon today

Option premium – price paid for the option Exercise price or strike price – the price at which the asset can be

bought or sold under the contract Open interest: number of outstanding options

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Option characteristics Expiration date

- European: can be exercised only at expiration- American: exercised any time before expiration

Option holder: long the option positionOption writer: short the option position

Hedged position: option transaction to offset the risk inherent in some other investment (to limit risk) Speculative position: option transaction to profit from the inherent riskiness of some underlying asset.

Option contracts are a zero sum game before commissions and other transaction costs.

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Call buyer (seller) expects the price of the underlying security to increase (decrease or stay steady)

Put buyer (seller) expects the price of the underlying security to decrease (increase or stay steady)

At option maturity- Option may expire worthless, be exercised, or be

sold

How Options Work

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Options Trading Option exchanges are continuous primary and

secondary markets- Chicago Board Options Exchange largest

Standardized exercise dates, exercise prices, and quantities- Facilitates offsetting positions through Options

Clearing CorporationOCC is guarantor, handles deliveries

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Options Contracts: Preliminaries

A call option is: In-the-money

- The exercise price is less than the spot price of the underlying asset.

At-the-money- The exercise price is equal to the spot price of the

underlying asset. Out-of-the-money

- The exercise price is more than the spot price of the underlying asset.

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Options Contracts: Preliminaries

A put option is: In-the-money

- The exercise price is greater than the spot price of the underlying asset.

At-the-money- The exercise price is equal to the spot price of the

underlying asset. Out-of-the-money

- The exercise price is less than the spot price of the underlying asset.

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OptionsExample: Suppose you own a call option with an exercise (strike) price of

$30. If the stock price is $40 (in-the-money):

- Your option has an intrinsic value of $10 - You have the right to buy at $30, and you can exercise and then sell

for $40. If the stock price is $20 (out-of-the-money):

- Your option has no intrinsic value- You would not exercise your right to buy something for $30 that you

can buy for $20!

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Options

Example: Suppose you own a put option with an exercise (strike) price of $30.

If the stock price is $20 (in-the-money):- Your option has an intrinsic value of $10 - You have the right to sell at $30, so you can buy the stock at

$20 and then exercise and sell for $30 If the stock price is $40 (out-of-the-money):

- Your option has no intrinsic value- You would not exercise your right to sell something for $30 that

you can sell for $40!

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Options

Stock Option Quotations- One contract is for 100 shares of stock- Quotations give:

Underlying stock and its current priceStrike priceMonth of expirationPremiums per share for puts and callsVolume of contracts

Premiums are often small- A small investment can be “leveraged” into high profits

(or losses)

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OptionsExample: Suppose that you buy a January $60 call option on Hansen

at a price (premium) of $9.Cost of your contract = $9 x 100 = $900If the current stock price is $63.20, the intrinsic value is $3.20 per

share. What is your dollar profit (loss) if, at expiration, Hansen is selling

for $50?Out-of-the-money, so Profit = ($900) What is your percentage profit with options?Return = (0-9)/9 = -100% What if you had invested in the stock?Return = (50-63.20)/63.20 = (20.89%)

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OptionsWhat is your dollar profit (loss) if, at expiration, Hansen is selling for $85?Profit = 100(85-60) – 900 = $1,600 Is your percentage profit with options?Return = (85-60-9)/9 = 77.78% What if you had invested in the stock?Return = (85-63.20)/63.20 = 34.49%

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Options Payoff diagrams

- Show payoffs at expiration for different stock prices (S) for a particular option contract with a strike price of E

- For calls:if the S<E, the payoff is zeroIf S>E, the payoff is S-EPayoff = Max [0, S-E]

- For puts:if the S>E, the payoff is zeroIf S<E, the payoff is E-SPayoff = Max [0, E-S]

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Option Trading Strategies

There are a number of different option strategies: Buying call options Selling call options Covered call Buying put options Selling put options Protective put

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Buying Call Options Position taken in the expectation that the price will increase (long

position) Profit for purchasing a Call Option:Per Share Profit =Max [0, S-E] – Call Premium The following diagram shows different total dollar profits for

buying a call option with a strike price of $70 and a premium of $6.13

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Buying Call Options

40 50 60 70 80 90 100

1,000

500

0

1,500

2,000

2,500

3,000

(500)

(1,000)

Exercise Price = $70Option Price = $6.13

Profit from Strategy

Stock Price at Expiration

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Selling Call Options Bet that the price will not increase greatly – collect

premium income with no payoff Can be a far riskier strategy than buying the same options The payoff for the buyer is the amount owed by the writer

(no upper bound on E-S) Uncovered calls: writer does not own the stock (riskier

position) Covered calls: writer owns the stock Moderately bullish investors sell calls against holding

stock to generate income

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Selling Call Options

40 50 60 70 80 90 100

(1,000)

(1,500)

(2,000)

(500)

0

500

1,000

(2,500)

(3,000)



Profit from Uncovered Call Strategy

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Covered callS< E S>E

Payoff of stock S SPayoff call -0 -(S-E)Premium C CTotal payoff C+S C+E

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Covered Call Writing

0 Stock Priceat Expiration

Profit ($)Purchased share

Written call

Combined

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Buying Put Options Position taken in the expectation that the price will

decrease (short position) Profit for purchasing a Put Option:Per Share Profit = Max [0, E-S] – Put Premium Protective put: Buying a put while owning the stock (if the

price declines, option gains offset portfolio losses)

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Buying Put Options

40 50 60 70 80 90 100

1,000

500

0

1,500

2,000

2,500

3,000

(500)

(1,000)




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Hedging strategy that provides a minimum return on the portfolio while keeping upside potential

Buy protective put that provides the minimum return - Put exercise price greater or less than the current

portfolio value? Problems in matching risk with contracts

Portfolio Insurance

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Protective put

S< E S>EPayoff of stock S S Payoff put E-S 0

Premium -P -PTotal payoff E-P S-P

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Selling Put Options Bet that the price will not decline greatly – collect

premium income with no payoff The payoff for the buyer is the amount owed by the writer

(payoff loss limited to the strike price since the stock’s value cannot fall below zero)

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Selling Put Options

40 50 60 70 80 90 100

(1,000)

(1,500)

(2,000)

(500)

0

500

1,000

(2,500)

(3,000)




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Exam type questionAn investor bought two Google June 425 (exercise price is $425) put

contracts for a premium of $20 per share. At the maturity (expiration), the Google stock price is $370.

(i) Draw the payoff diagram of the investment position.(ii) Calculate the total profit/loss of the position at the expiration.

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Option pricing Factors contributing value of an option

- price of the underlying stock- time until expiration- volatility of underlying stock price- cash dividend- prevailing interest rate.

Intrinsic value: difference between an in-the-money option’s strike price and current market price

Time value: speculative value. Call price = Intrinsic value + time value

Exercise prior to maturity implies the option owner receives intrinsic value only, not time value

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Variable Call Put Stock Price + - Exercise Price - + Time to maturity + + Stock volatility + + Interest rates + - Cash dividends - +

Factors Affecting Prices

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Black-Scholes Option Pricing Model

Where C: current price of a call option S: current market price of the underlying stock X: exercise price r: risk free rate t: time until expiration N(d1) and N (d2) : cumulative density functions for d1 and d2

)()( 21 dNeXdNSC rt

funds invested ofcost yOpportunit

potential upside of Value

priceCall

t

trXSd

2

15.0ln

tdd 12

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Options can be used to control the riskiness of common stocks- If stock owned, sell calls or buy puts

Call or put option prices do not usually change the same dollar amount as the stock being hedged- Shares purchased per calls written =N(d1)- Shares purchased per puts purchased =N(d1) - 1

Riskless Hedging(NOT on the exam)

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Learning outcomes:• discuss the benefits of using financial derivatives • know the basic characteristics of options• know the options’ payoffs• know how to calculate the profits/losses of a long/short call and

put options, covered call and protective put (numerical application)

• Know the factors affecting option pricing; no numerical problems with Black-Scholes

NOT on the exam: Boundaries on option prices p523-524; Put option valuation, riskless hedging, Stock index options p 528-534; Recommended End-of-chapter questions:19-1 to 14• Recommended End-of-chapter problems:19.1, 2, 3

Documents

Options (Chapter 19 Jones)