Download pdf - Class Notes Option Basics

7/29/2019 Class Notes Option Basics

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Option Basics

Goals

What are options? Why are they useful? How

are they valued?

Why do we care?

Option valuation is useful both directly andconceptually in many aspects of finance.

Capital Structure

Capital budgeting (real options, embedded options)

Hedging and risk management Hedging vs. Speculating

Agency Problems

All these slides (slides1-38) are covered in the Option

Basics lecture video (43:10 long)


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Options and Derivatives Derivatives are simply a class of securities whose

prices are determined from the prices of otherassets. The asset on which the derivatives value isbased is called the underlying orprimary asset.

Options, futures, and swaps are just some examples

of derivatives Options are traded on various underlying assets.

Individual stocks as well as stock indexes

Futures, Foreign currency, Interest rates Financial engineering is the practice of combining

derivatives to construct specialized financial

arrangements


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Option Contracts

Acall option gives the holder the right

(but not the obligation) to buy an asset for

a specified price (strike or exercise price)on or before a specified expiration date.

Example: A MSFT July 120 call would givethe buyer the right to purchase 100 shares of

MSFT stock at $120 per share on or before

the third Friday in July.

Why would someone want to buy this

option?


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Call Options Call options give investors the right to BUY

an asset at a fixed strike price on or before an

expiration date. Investors would choose to purchase call

options for many reasons. However, the most

obvious is that they expect the stock willincrease above the strike price before theexpiration date of the option.

Why would someone buy the July $120 MSFTcall? They expect that MSFT will trade above$120 per share BEFORE the third Friday in July.


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Option Contracts

Aput option gives the holder the right (but not

the obligation) to sell an asset for a specified

price (strike or exercise price) on or before a

specified expiration date.

Example: An INTC September 95 put would givethe buyer the right to sell 100 shares of INTC

stock at $95 per share on or before the third

Friday in September.

Why would someone want to buy this option?


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Put Options

Put options give investors the right to SELLan asset at a fixed strike price on or before anexpiration date.

Investors would choose to purchase putoptions for many reasons. However, the most

obvious is that they expect the stock price willdecrease below the strike price before theexpiration date of the option.

Why would someone buy the INTC September$95 put? They expect that INTC will trade below$95 per share BEFORE the third Friday in

September.


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Some Terminology In order for someone to buy an option, someone must be

willing to sell it (options are zero sum games). Selling anoption is also known as writing the option, and the seller

of an option is called the writer of the option. Because option writers give the buyers the right to exercise,

writers areobligatedto fulfill their commitment.

Thus, the option aspect (i.e. choice of what to do) of options is

really given to the buyer and the writer is forced to live with thebuyers decision.

An option is in the money when its exercise would

produce a positive payoff. An option isout of the money when its exercise would

produce a negative payoff.

The option isat the money when the price of theunderlying asset equals the strike price of the option.


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Terminology The price paid for an option contract is called the

premium.

Option contracts on stock are generally for 100

shares, but quoted on a per share basis. Thus, if the quote for an option is $5, the cost of

purchasing that option is $500 because it is $5 pershare for 100 shares.

AnAmerican option allows its holder to exerciseit on or before the expiration date.

AEuropean option can only be exercised on theexpiration date.

However, both American and European optionscan always be sold prior to expiration.


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Quick Review When would a call option be in the money? Out of the money? At the

money?

For call options:

In the money

underlying asset price is above the option strike price Out of the money underlying asset price is below the option strike price

At the money underlying asset price exactly equals the option strike price

What about a put option?

For put options: In the money underlying asset price is below the option strike price

Out of the money underlying asset price is above the option strike price

At the money underlying asset price exactly equals the option strike price

Why would investors write (sell) options?

Investors would write (i.e. sell) options in order to get paid the premium.

They would do this if they expect that the option they write will expire

out of the money and thus the investor they sell the option to wont

exercise against them.


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Quick Review

If you wanted to have the option to purchase 800 shares ofMSFT, how many calls would you need to buy?

To have the option to purchase 800 shares of MSFT, youwould need to buy 8 calls since each option is for 100

shares. What is the difference between an American and a

European option?

The only difference between an American and Europeanoption is when you can exercise it. American options can

be exercised at any time, European options can only beexercised on the expiration date (both can be sold at any

time however) What are the three things an option holder can do with

their option?

The three things an option holder can do are: 1. Sell theoption, 2. Exercise the option, or 3. Let the option expire.


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The Value of Options

The value of an option (either a put or a call)is comprised of two components

The intrinsic value This is the value associated with exercising the option

immediately and simultaneously trading the

underlying asset. In the money (At and Out of the money) options havepositive (zero) value from exercising immediately.

The value of waiting to exercise.

This essentially captures the option part of an

option. Since you can choose to exercise or not, that

flexibility has value. The value of that flexibility

must be non-negative.


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The Value of Options Jan $17.50 Call

Lets look at the Jan 05 $17.50 call. The option gives you the right to buy thestock for $17.50 per share, but the stock is CURRENTLY selling for $18.70.Exercising this option would allow you to buy the stock for $17.50 from theoption writer. You could then turn around and sell it in the market for $18.70

per share. This would give you an immediate profit of $1.20. This $1.20 isexactly what we call the intrinsic value of the option (and reflects that theoption is in the money). It is the value associated with immediate exercise.

Since the price of the option is $1.80 while the intrinsic value is only $1.20, itmeans that the value associated with waiting to exercise is $0.60. The optiondoesnt expire until the third Friday in January, so we can choose to wait toexercise it. Given the option price, the value of having that flexibility is $0.60.

Cisco Systems - Nov 11th, 04 Call Prices Put Prices

Stock Price Strike Price Jan 05 Apr 05 Jan 05 Apr 05

$18.70 $15.00 $3.90 $4.10 $0.30 $0.50$18.70 $17.50 $1.80 $2.30 $0.90 $1.75

$18.70 $20.00 $0.60 $1.05 $2.15 $3.80

$18.70 $22.50 $0.15 $0.40 $4.00 $6.50

On November 11th

, 2004, Cisco Systems stock was trading at $18.70.Below are option prices on that date.


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The Value of Options April $20 Call

Lets look at the April 05 $20 call. The option gives you the right tobuy the stock for $20.00 per share, but the stock is CURRENTLYselling for $18.70. This means that you could buy the stock in theopen market for $18.70. You would never choose to exercise thisoption and pay the option writer $20 per share. There is no value of

exercising this option immediately. Hence, the intrinsic value of theJan $20 call is $0 (and thus why this option is out of the money).

However, the price of the option is $1.05. The value comes from theflexibility of waiting. The option doesnt expire until the third Fridayin April and the value of waiting to exercise is worth $1.05.

Cisco Systems - Nov 11th, 04 Call Prices Put PricesStock Price Strike Price Jan 05 Apr 05 Jan 05 Apr 05

$18.70 $15.00 $3.90 $4.10 $0.30 $0.50

$18.70 $17.50 $1.80 $2.30 $0.90 $1.75

$18.70 $20.00 $0.60 $1.05 $2.15 $3.80

$18.70 $22.50 $0.15 $0.40 $4.00 $6.50


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The Value of Options Jan $17.50 Put

Lets look at the Jan 05 $17.50 put. The option gives you the right to

sell the stock for $17.50 per share, but the stock is CURRENTLYselling for $18.70. This means that you could sell the stock in theopen market for $18.70. Thus, you would never choose to exercisethis option and sell the stock to the option writer for only $17.50 pershare. There is no value of exercising this option immediately.

Hence, the intrinsic value of the Jan $17.50 put is $0 (and thus whythis option is out of the money).

However, the price of the option is $0.90. The value comes from theflexibility of waiting. The option doesnt expire until the third Friday

in January and the value of waiting to exercise is worth $0.90.


$18.70 $15.00 $3.90 $4.10 $0.30 $0.50

$18.70 $17.50 $1.80 $2.30 $0.90 $1.75

$18.70 $20.00 $0.60 $1.05 $2.15 $3.80

$18.70 $22.50 $0.15 $0.40 $4.00 $6.50


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The Value of Options April $20 Put

Lets look at the April 05 $20 put. The option gives you the right to sell

the stock for $20 per share, but the stock is CURRENTLY selling for$18.70. You could buy the stock in the open market for $18.70. Youcould then immediately exercise this option, which would allow you tosell the stock to the option writer for $20. This would give you animmediate profit of $1.30. This $1.30 is exactly what we call the

intrinsic value of the option (and reflects that the option is in themoney). It is the value associated with immediate exercise.

Since the price of the option is $3.80, it means that the value associatedwith waiting to exercise is $2.50. The option doesnt expire until thethird Friday in April, so we can choose to wait to exercise it. Given the

option price, the value of having that flexibility is $2.50.


$18.70 $15.00 $3.90 $4.10 $0.30 $0.50

$18.70 $17.50 $1.80 $2.30 $0.90 $1.75

$18.70 $20.00 $0.60 $1.05 $2.15 $3.80

$18.70 $22.50 $0.15 $0.40 $4.00 $6.50


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Intrinsic Value vs. Value of Waiting

Cisco Systems - Nov 11th

, 04 Call Prices Put PricesStock Price Strike Price Jan 05 Apr 05 Jan 05 Apr 05

$18.70 $15.00 $3.90 $4.10 $0.30 $0.50

$18.70 $17.50 $1.80 $2.30 $0.90 $1.75

$18.70 $20.00 $0.60 $1.05 $2.15 $3.80

$18.70 $22.50 $0.15 $0.40 $4.00 $6.50

Intrinsic Values Calls Puts

Stock Price Strike Price Jan 05 Apr 05 Jan 05 Apr 05

$18.70 $15.00 $3.70 $3.70 $0 $0$18.70 $17.50 $1.20 $1.20 $0 $0

$18.70 $20.00 $0 $0 $1.30 $1.30

$18.70 $22.50 $0 $0 $3.80 $3.80

Value of Waiting Calls PutsStock Price Strike Price Jan 05 Apr 05 Jan 05 Apr 05

$18.70 $15.00 $0.20 $0.40 $0.30 $0.50

$18.70 $17.50 $0.60 $1.10 $0.90 $1.75

$18.70 $20.00 $0.60 $1.05 $0.85 $2.50$18.70 $22.50 $0.15 $0.40 $0.20 $2.70


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Intrinsic Value vs. Value of Waiting Notice that the price of every option is greater than its

intrinsic value. If that were not true, there would be an arbitrage opportunity.

You could simply buy the option, immediately exercise it, andsimultaneously trade the shares in the market. If prices are less

than intrinsic value, that strategy would generate riskless profits.Thus, we dont see this exist in reality.

For calls (puts), the intrinsic value is higher when the strikeprice decreases (increases). The right to buy (sell) at a lower (higher) price is more valuable,

all else equal.

Notice that the length of time to expiration has no impact on theintrinsic value of the option.

For both calls and puts, notice that the value of waiting ishigher for the April options than the corresponding Januaryoption with the same strike price. Having a longer time to over which to potentially exercise is more

valuable than having a shorter time.


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How to Value Options As we have seen, there are two components to

option value: the intrinsic value, and the value ofwaiting to exercise.

If we know how to determine these values, we canfigure out what the value of an option should be.

Of the two, the intrinsic value is easier tocalculate. As such, lets first focus on that. One way to do this is to look at options immediately

before they expire. At that point in time, the value ofwaiting to exercise is zero because if you wait, the

option expires worthless. We will look at the payoutsand profits associated with different options at thepoint of expiration. Well come back to the value ofwaiting to exercise later, after we have a better handle

on these strange securities.


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Value of Call Options at Expiration To examine this issue in a general framework, we

need to develop some notation.

Recall that call options give the holder the right topurchase a security at the exercise price. We willdenote the price of the underlying security (atexpiration time T) as ST and the exercise price as X

Since the option need not be exercised, the value iscontingent on the relative values of ST and X.

Recall that to purchase the call, an investor must

pay the premium (to the writer) which we willdenote by C (for calls) or P (for puts). The amount of the premium will be the difference

between looking at the payoffs of an option and theprofits associated with the option.


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Value of Call Options at Expiration

Payoffs to: Call Buyer Call WriterIn the money(ST > X) ST X - (ST X)Out of (or at) the money (ST X)

0 0Overall: Max[0, ST-X] Min[0, X-ST]

Profits to: Call Buyer Call WriterIf ST > X (in the money) (ST X) C - (ST X)+CIf ST X (at or out of money) - C C

Overall Max[0,ST -X]-C Min[0,X-ST]+C


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Value of Call Options at Expiration Suppose you bought a MSFT 120 call for $13.

What are the payoffs and profits at expiration forcertain stock prices?

Realize that only one of these prices can occurwe wantto examine possibilities though.

Stock Price Call Value Profit

Buyer

Profit

Writer110 0 -13 13120 0 -13 13

130 10 -3 3133 13 0 0140 20 7 -7

150 30 17 -17


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(Buyer)

-20

0

20

40

85 95 105 115 125 135 145 155

payoff profit

Max [0, ST-X] Max [0, ST-X] - C

X = Exercise price = $120 C = Call premium = $13

Price per share of MSFT on expiration date

X + C

120 + 13 = 133

X = $120


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Value of Call Options at Expiration Notice that the value of the call option is $0 until the stock reaches

the strike price of $120. Then, the value of the option increasesdollar for dollar with the stock. The resulting graph looks somethinglike a hockey stick.

However, in order for someone to buy this option, they would have

had to pay the seller $13 up front. Thus, even though the option isvaluable for prices of MSFT above $120, the call buyer will have lostmoney unless the stock price rises above $133 (which is X + C).When MSFT stock is $133 at expiration, the option will be worthexactly $13, which is the same price at which the buyer purchased theoption, so that is the breakeven point. To see why the option would be worth $13 if MSFT is at $133 realize that the

option allows the buyer to buy the stock at $120 per share. If the stock istrading at $133 per share, buying at $120 is something the buyer would want todo. In fact, it is worth $13 per share to have that benefit and thus, the price of

the option is $13. Notice that buying a call option has a limited downside. The most a

buyer can lose is the $13 if the option expires worthless. However,there is unlimited upside, since there is technically no limit to how

high a stock price can be.


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(Writer)

-40-30

-20-10

01020

85 95 105 115 125 135 145 155

payoff profitMin [0, X-ST] Min [0, X-ST] + C

X = Exercise price = $120 C = Call premium = $13

Price per share of MSFT on expiration date

X = $120

X + C

120 + 13 = 133


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The graph for the seller is simply the mirror image of the one for thebuyer. Remember that options are zero sum games.

The option seller would have received the $13 premium up front and

would be hoping that the option expires worthless. Thus, as long as

MSFT shares are lower than $133 (X + C) by expiration, the sellerwould have made money.

To see this, consider if MSFT was selling at $133. The option writer would

have given the buyer the right to buy the stock at $120 per share. Thus, the

seller would be obligated to fulfill this promise and sell the buyer shares for

$120 each. However, the market value is $133, so selling the shares at $120

results in a loss of $13 per share. However, the option writer received a

premium of $13 per share when he sold the option, so he effectively has broken

even (ignoring time value of money for the moment)

However, notice that the seller has limited upside potential. The

most he can make is $13 if the option expires worthless. On the other

hand, a seller has unlimited downside risk because there is no limit

how high a stock can go.


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Selling Call Options

Selling a call option gives someone else the right to buystock from you. Sellers either already own shares of thestock or they dont.

If you sell a call option on stock you already own, you are said tohave written acoveredcall. You are covered because no matterhow high the price of the stock goes, you already own shares thatyou can sell to the call buyer if they choose to exercise their

option. If you sell a call option on a stock that you dont already own, you

are said to have written anakedcall. You are naked becausewithout owning the stock already, you are fully exposed to the

price changes in the stock. You would need to go into the marketand purchase the stock at the prevailing price if the call buyerchooses to exercise their option. Writing naked calls is risky since call writers have limited upside, but

unlimited downside. Most brokers will require you to post margin if youtry to write naked calls.


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Value of Put Options at Expiration

Payoffs to: Put Buyer Put WriterOut of (or at) the money(ST X) 0 0In the money (ST < X) X ST - (X ST)

Overall: Max[0,X-ST] Min[0,ST-X]

Profits to: Put Buyer Put Writer

If ST X (at or out of the money) -P P

If ST < X(in the money)

X- ST - P -(X - ST) + POverall Max[0,X-ST]-P Min[0,ST-X]+P


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Suppose you bought an INTC 95 put for $9.What are the payoffs and profits at expiration

for certain stock prices?StockPrice

PutValue

ProfitBuyer

ProfitWriter

65 30 21 -2175 20 11 -11

85 10 1 -186 9 0 0

95 0 -9 9

105 0 -9 9


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(Buyer)

-10

01020

304050

55 65 75 85 95 105 115 125

option value profitMax [0, X ST] Max [0, X ST] - P

X = $95

X P = 95 9 = 86

X = Exercise price = $95 P = Put premium = $9


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Value of Put Options at Expiration Notice that the value of the put option is $0 as long as the stock is

above the strike price of $95. Below $95, the value of the optionincreases one dollar for every dollar decrease of the stock.

However, in order for someone to buy this option, they would havehad to pay the seller $9 up front. Thus, even though the option is

valuable for prices of INTC below $95, the put buyer will have lostmoney unless the stock price falls below $86 (which is X - P). WhenINTC is $86 at expiration, the option will be worth exactly $9, whichis the same price at which the buyer purchased the option, so that isthe breakeven point. To see why the option would be worth $9 if INTC is at $86 realize that the

option allows the buyer to sell the stock (to the option writer) at $95 per share.If the stock is trading at $86 per share, selling at $95 is something the option

buyer would want to do. In fact, it is worth $9 per share to have that benefit andthus, the price of the option is $9.

Notice that buying a put option has a limited downside. The most abuyer can lose is the $9 if the option expires worthless. However,unlike buying a call option, buying a put option provides a limitedupside. The reason is that the value of the stock can never decrease

below zero, so the value of the put is inherently limited.


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(Writer)

-50

-40

-30

-20

-10

0

10

20

55 65 75 85 95 105 115 125

payoff profit

Min [0, ST - X ] Min [0, ST - X] + P

X = $95

X P = 95 9 = 86

X = Exercise price = $95 P = Put premium = $9


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The graph for the seller is simply the mirror image of the one for thebuyer. Remember that options are zero sum games.

The option seller would have received the $9 premium up front and

would be hoping that the option expires worthless. Thus, as long as

INTC shares are higher than $86 (X - P) by expiration, the sellerwould have made money.

To see this, consider if INTC was selling at $86. The put writer would have

given the buyer the right to sell stock (to the writer) at $95 per share. Thus, the

put writer would be obligated to fulfill this promise and buy shares for $95each. However, the market value is $86, so buying the shares at $95 results in a

loss of $9 per share. However, the option writer received a premium of $9 per

share when he sold the option, so he effectively has broken even (ignoring time

value of money for the moment) However, notice that the seller has limited upside potential. The

most he can make is $9 if the option expires worthless. The sellers

downside is also somewhat limited because the stock can never sell

below $0.


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Factors that Impact Option Values So far, we have seen that at expiration, the value of

options are dependent on the relative values of thestrike price (X) and the stock price (S). This leads

us to the first two factors that impact option values.There will be others we examine later.

Exercise price: X The lower the exercise price, the higher (lower) the call

(put) value

Stock price: S The higher the stock price, the higher (lower) the call

(put) value We also saw that time to expiration (T) mattered.

The longer time to expiration, the more valuable the

option. This is true for BOTH calls and puts.


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Portfolios of OptionsMany complex payoff structures can be createdusing combinations of calls and puts. Spreads,straddles, collars, etc.

How can we determine the payoff structure (atexpiration) of a portfolio of options? A three stepprocess

1. Calculate the intrinsic value ofeach individualoption at the exercise price of every option in the

portfolio, aprice above the the highest strike price,and aprice below the lowest strike price.

2. Add the payoffs of all the options together to get thetotal payoff to the portfolio. Graph these points

3. Connect the dots with straight lines. For pricesbelow and above the range, extend the straight lines.


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Example of Combination of Options

Consider the following combination for a stockthat currently sells at $50 Sell $50 call

Sell $50 put

Buy $40 put

Buy $60 call All options have the same time to expiration.

Determine value of each option at every exerciseprice (40, 50, & 60), a price above the highest(something above 60, i.e. 70), and a price below

the lowest (something below 40, i.e. 30). Essentially, determine the intrinsic value at each of

those points (30, 40, 50, 60, & 70) and graph them

against the stock value.


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Example of Combination of Options

OptionStock Price

30 40 50 60 70

Sell 50 Call 0 0 0 -10 -20

Sell 50 Put -20 -10 0 0 0

Buy 40 Put 10 0 0 0 0

Buy 60 Call 0 0 0 0 10

Sum -10 -10 0 -10 -10


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Option Payoff Diagram

30 40 50 60 70

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

Value

ofPortfol

io

Under lying Price

This option portfolio is known as a butterfly spread. Look at the

graph with a creative eyesort of a butterfly with wings.

P tf li f O ti B tt fl S d


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Portfolio of Options Butterfly Spread Notice that the payoffs from this portfolio range from 0 to a loss of

10. In other words, the payoff (at expiration) to this portfolio isNEVER positive. Why would anyone choose to take such a position? Dont forget that you are buying 2 options and selling 2 options. When you

buy options, you pay the premiums, when you sell them, you receive the

premiums. Since the payoff of the portfolio is always negative, the only reasonsomeone would do this is because they are receiving money up front when theyenter the position. Itmustbe the case that the premiums you get from selling the 50 call and 50 put are

greater than the premiums you pay from buying the 60 call and 60 put. If that is nottrue, arbitrage profits can be made

Notice also that the amount by which the premiums you get exceed the premiumsyou paymustbe less than $10. Since the most negative the payoff can be is $10,you cant be paid more than this to enter the position, otherwise arbitrage willoccur.

Technically, the premiums must be less than the present value of $10 because time valueof money matters.

Investors might enter a butterfly spread if they believed that the price of theunderlying asset was not going to change dramatically before the expirationdate. Notice that the highest payoff (although that is $0) of the portfolio iswhen the price of the stock remains at 50. At that price, the investor would pay$0 and get to keep all of the premiums they collected up front. Essentially a

butterfly spread is a bet that volatility will be low.