Vicentiu Covrig 1 Options Options (Chapter 18 Hirschey and Nofsinger)
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Transcript of Vicentiu Covrig 1 Options Options (Chapter 18 Hirschey and Nofsinger)
Vicentiu Covrig
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OptionsOptions(Chapter 18 Hirschey and Nofsinger)(Chapter 18 Hirschey and Nofsinger)
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Potential Benefits of DerivativesPotential 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 characteristicsOption characteristics 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 Long-term Equity AnticiPation Securities (LEAPS): expiration dates up to three
years.
- Long-term calls and puts.
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Option characteristicsOption characteristics Expiration date
- European: can be exercised only at expiration
- American: exercised any time before expiration
Option holder: long the option position
Option 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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Options Contracts: PreliminariesOptions 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: PreliminariesOptions 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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OptionsOptions
Example: 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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OptionsOptions
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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OptionsOptions
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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OptionsOptionsExample: 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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OptionsOptionsWhat 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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OptionsOptions Payoff diagrams
- Show payoffs at expiration for different stock prices (V) for a particular option contract with a strike price of X
- For calls:if the V<X, the payoff is zeroIf V>X, the payoff is V-XPayoff = Max [0, V-X]
- For puts:if the V>X, the payoff is zeroIf V<X, the payoff is X-VPayoff = Max [0, X-V]
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Option Trading StrategiesOption Trading Strategies
There are a number of different option strategies: Buying call options Selling call options Buying put options Selling put options Option spreads
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Buying Call OptionsBuying 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, V-X] – 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 OptionsBuying 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 = $70
Option Price = $6.13
Profit from Strategy
Stock Price at Expiration
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Selling Call OptionsSelling 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 V-X) 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 OptionsSelling Call Options
40 50 60 70 80 90 100
(1,000)
(1,500)
(2,000)
(500)
0
500
1,000
(2,500)
(3,000)
Exercise Price = $70
Option Price = $6.13
Stock Price at Expiration
Profit from Uncovered Call Strategy
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Buying Put OptionsBuying 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, X-V] – 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 OptionsBuying Put 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 = $70
Option Price = $2.25
Profit from Strategy
Stock Price at Expiration
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Selling Put OptionsSelling 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 OptionsSelling Put Options
40 50 60 70 80 90 100
(1,000)
(1,500)
(2,000)
(500)
0
500
1,000
(2,500)
(3,000)
Exercise Price = $70
Option Price = $2.25
Stock Price at Expiration
Profit from Strategy
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Exam type questionExam type question
An 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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Combinations Combinations Spread: both buyer and writer of the same type of
option on the same underlying asset- Price spread: purchase or sale of options on the same
underlying asset but different exercise price
- Time spread: purchase or sale of options on the same underlying asset but different expiration dates
Bull call spread: purchase of a low strike price call and sale of a high strike price call.
Bull put spread: sale of high strike price put and purchase or a low strike price put
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Payoff Long call
Short call
Bull call spread
PayoffLong put
Short put
Bull put spread
Payoff
Long call Short put
Straddle
Straddle : purchasing a call andWriting a put on the same asset,
exercise price, and expiration date
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Option pricingOption 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
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Black-Scholes Option Pricing ModelBlack-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 dNe
XdNSC
rt
funds invested of
cost yOpportunit
potential upside
of Value
price
Call
t
trXSd
2
1
5.0ln tdd 12
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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 (numerical application) •Know the factors affecting option pricing (slide 24); no numerical problems with Black-Scholes•Recommended End-of-chapter questions: 18.1, 18.4,18.6• Recommended End-of-chapter problems: 18.7, 18.8, 18.9, 18.10