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					                                                                                               MFIN 6663
                                                                                   Sobey School ofBusiness
                                                                                   Saint Mary’s University
                                                                                          Greg MacKinnon
Options
Options are an example of a type of security referred to as a derivative security. Derivative
securities have no value in and of themselves, they only have value because they are in some
way related to other securities. That is, they derive their value from another security.
An option is simply a financial contract. One party writes the option and then sells it to another
party. It gives the holder of the option the right, but not the obligation, to buy or sell (depending
on the type of option) an asset at a fixed price, on or before a certain date. Note that the holder
of the option is not obligated to do anything. If it would not be wise to use the option then he or
she can throw it away.

There exists an organized exchange for the trading of options, and the options market has
developed its own lexicon:

Definitions:
                1. Call Option: This type of option gives the holder the right, but not the
                   obligation, to buy an asset at a fixed price from the seller of the option (the
                   seller of an option writes the option, and is referred to as the writer).
                2. Put Option: This type of option gives the holder the right, but not the
                   obligation, to sell an asset at a fixed price to the writer of the option. (Note
                   that the writer of an option is obligated to fulfill his part of the contract if the
                   holder desires to use the option. Thus, for a put option, if the holder wants to
                   sell the asset at the fixed price, the writer must buy it. The same holds for a
                   call option.)
                3. Underlying Asset: This is the asset (most often a stock) on which the option
                   is written. It is this asset that the holder of the option has the right to buy/sell.
                   For example, an option written on a particular stock is referred to as a stock
                   option.
                4. Exercising the Option: This is the act of the holder using the option to
                   buy/sell the underlying asset.
                5. Exercise Price or Strike Price: The fixed price in the option at which the
                   holder can buy/sell. This is set at the time the option is written and cannot be
                   changed.
                6. Expiration Date or Maturity Date: The option must be exercised on or
                   before the expiration date. After this, it expires and becomes worthless.
                7. Premium: The price paid to the writer in order to obtain the option.
                8. a) American Option: This type of option (either put or call) can be
                         exercised at anytime up to the expiration date. This is (by far) the
                         most common type of stock option.
                    b) European Option: This type of option (either put or call) can be
                         exercised only on the expiration date.
                                                                                                MFIN 6663
                                                                                    Sobey School ofBusiness
                                                                                    Saint Mary’s University
                                                                                           Greg MacKinnon


Call Options
Assume that someone writes a call option on Ford Motor Co. stock. The holder of the option
has can buy a share of Ford at a strike price of $60 on or before June 30, 1995.
Let the expiration date be T (equal to June 30 in this case). Let the price of the stock at time T
be ST ( and the price is St at any other time). What is the value of the option at the expiration
date? The value of the option will depend on S T .
        If ST  $60; it is cheaper for the holder to buy the stock on the open market rather than
        use the option. The holder will therefore let the option expire without using it. The call is
        worthless.

        If ST > $60; the holder exercises the option and buys a share of Ford at $60, then sells
        it in the open market for ST to make a profit. The value of the call is this profit, (S T -
        60).

If, at any time during the life of the call option the stock price is greater than the strike price (S t
> $60), the call is said to be in the money. That is, at the current stock price it would be
profitable to exercise the option.
If, at any time during the life of the call option the stock price is less than the strike price (S t <
$60), the call is said to be out of the money. That is, at the current stock price it would not be
profitable to exercise the option.
If the stock price is equal to the strike price the option is said to be at the money. Also, at
stock prices far above the strike the call option is deep in the money and deep out of the
money if the stock price is far below the strike.

Summary:
      Let K be the strike price of a call option.

                           Value of a Call Option at the Expiration Date
                                0               ,        if ST  K
                                ST - K          ,        if ST > K

If ST  K, then there is limited liability for the holder of the option. No matter how low the stock
price goes, you cannot lose any more money.

Graphically:
       Value of Call
       Option at
       Expiration




                                                                                    ST
                                                 K
                                                                                            MFIN 6663
                                                                                Sobey School ofBusiness
                                                                                Saint Mary’s University
                                                                                       Greg MacKinnon




This type of graph for options is termed a Bachelier diagram.

Put Options
Assume that someone writes a put option on Ford Motor Co. stock that allows the holder to
sell a share of Ford on or before the expiration date, T, at a fixed price of K.
What is the value of the put option on the day that it expires?

        If ST < K, the holder buys the stock on the open market at ST and sells it to the option
        writer (i.e. exercises the put) for K. The value of the put option is then (K - ST ).

        If ST  K, the holder would be better off selling any stock in the open market rather
        than through the option. Thus the put option is worthless.

Summary:
                          Value of a Put Option at the Expiration Date
                               K - ST          ,        if ST < K
                               0               ,        if ST  K

Graphically:


     Value of a Put
     Option at
     Expiration

                  K




                                                                           ST
                                     K



Writing Options
In every option there are two sides, the holder (or buyer) of the option, and the writer who is
obligated to buy/sell the stock to the holder if the holder wishes.
An option is really a zero-sum game in that whenever the holder of an option profits, the writer
loses and vice versa. Thus, we can examine the value of writing an option in the same way as
we looked at the value of owning an option. Graphically, the value of the writer’s position at the
expiration date of the option is simply the mirror image of the holder’s position.
                                                                                            MFIN 6663
                                                                                Sobey School ofBusiness
                                                                                Saint Mary’s University
                                                                                       Greg MacKinnon

             Value of Writing a Call at
             Expiration Date




                                          K
                   0                                                       ST




               Value of Writing Put
               at Expiration Date




                                      K
                   0                                                            ST




                   K



Note: The value to the writer is never greater than zero. Why does anyone write an option? The
writer gets a price (the premium) for the option when it is sold and this premium is not seen on
the diagrams. Thus, the writer hopes that the option finishes out of the money so that it is not
exercised and the writer keeps the premium.
                                                                                             MFIN 6663
                                                                                 Sobey School ofBusiness
                                                                                 Saint Mary’s University
                                                                                        Greg MacKinnon


Bachelier diagrams can be drawn in terms of profit at expiration (rather than in terms of value,
as we have done). In this way, the premium is included.




                where: C is the premium on the call
                       P is the premium on the put

Similarly, you can draw profit diagrams for writing calls and puts by shifting the diagrams up by
the premium.

Example: If you buy a call and it ends up that at the expiration date S T < K, you do not
exercise. But you lose $C, the price that you initially paid for the option.
If you wrote a call and ST < K, then you make a profit of $C as the call is not exercised and
you keep the premium that was paid to you initially.

The break-even points on the graphs above are those ending stock prices at which you would
earn zero profits. For a call, the break-even point is (K+C). For a put, the break-even point is
(K-P).

Example: Consider a call option that you purchased last month that expires today. The option
initially cost you $1.50.
                                                  K = $20
                                                 ST = $21
                                                 C = $1.50
Since ST >K, it is best for you to exercise the option. However, even though you exercise (i.e.
the option ends up in the money) you still lose money as:
                                                 ST < K+C
You get ($21 - $20) = $1 from exercising the option, but since you paid $1.50 for it you are
really losing $0.50 (it is still beneficial to exercise, though, because if you do not you lose the
entire $1.50).

				
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