Class Notes Option Basics

  • Published on
    14-Apr-2018

  • View
    212

  • Download
    0

Embed Size (px)

Transcript

  • 7/29/2019 Class Notes Option Basics

    1/38

    1

    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)

  • 7/29/2019 Class Notes Option Basics

    2/38

    2

    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

  • 7/29/2019 Class Notes Option Basics

    3/38

    3

    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?

  • 7/29/2019 Class Notes Option Basics

    4/38

    4

    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.

  • 7/29/2019 Class Notes Option Basics

    5/38

    5

    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?

  • 7/29/2019 Class Notes Option Basics

    6/38

    6

    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.

  • 7/29/2019 Class Notes Option Basics

    7/38

    7

    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.

  • 7/29/2019 Class Notes Option Basics

    8/38

    8

    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.

  • 7/29/2019 Class Notes Option Basics

    9/38

    9

    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.

  • 7/29/2019 Class Notes Option Basics

    10/38

    10

    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.

  • 7/29/2019 Class Notes Option Basics

    11/38

    11

    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.

  • 7/29/2019 Class Notes Option Basics

    12/38

    12

    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.

  • 7/29/2019 Class Notes Option Basics

    13/38

    13

    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

  • 7/29/2019 Class Notes Option Basics

    14/38

    14

    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.

    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

  • 7/29/2019 Class Notes Option Basics

    15/38

    15

    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.

    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

  • 7/29/2019 Class Notes Option Basics

    16/38

    16

    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

  • 7/29/2019 Class Notes Option Basics

    17/38

    17

    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.

  • 7/29/2019 Class Notes Option Basics

    18/38

    18

    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.

  • 7/29/2019 Class Notes Option Basics

    19/38

    19

    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.

  • 7/29/2019 Class Notes Option Basics

    20/38

    20

    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

  • 7/29/2019 Class Notes Option Basics

    21/38

    21

    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...