Options
• This PowerPoint presentation consists
of two examples.
– Put Option
– Call Option
• Options are part of a larger group of
securities known as derivatives. In
addition to options, derivatives consist
of futures and swaps.
Stock Option
•
•
Stock options tend to be the easiest type of derivatives to grasp. In
addition to stocks, options exist for a host of financial assets. Even in
the case of stocks, options may exist for individual stocks as well as
some of the major indices. We will begin with an example for an
individual stock (you should note, option prices are listed for individual
stocks though typically sell in lots of 100 shares).
Upon hearing some interesting news, suppose you believe IBM stock
was about to sky rocket. You have some extra money to invest right
now, but know that you’ll need the money – e.g., pay tuition – in three
months. Thus, you plan to hold the stock for only three months –
hence, we can ignore dividends and just focus on the capital gain or
loss resulting from the price of the stock.
Stock Option
•
•
The IBM stock is currently selling for $50 per share. Ignoring any
transactions costs (e.g., brokerage fees), what are your potential gains
and losses?
The answer is pretty clear, but we’ll create a little table anyway. What
would your profit and loss be if the price three months from now was
$40? $45? $50? $55? $60?
Stock Option
•
•
The IBM stock is currently selling for $50 per share. Ignoring any
transactions costs (e.g., brokerage fees), what are your potential gains
and losses?
The answer is pretty clear, but we’ll create a little table anyway. What
would your profit and loss be if the price three months from now was
$40? $45? $50? $55? $60?
3 Month
Current
Profit or
Price
Price
Loss
$40
$50
-$10
$45
$50
-$5
$50
$50
$0
$55
$50
+$5
$60
$50
+$10
Now, plot this on a graph…
Stock Option
Along the horizontal axis, plot the various prices of the stock. Along the
vertical axis plot…
Price
40
45
50
55
60
Stock Option
Along the horizontal axis, plot the various prices of the stock. Along the
vertical axis plot…the profit (gain) and loss for each ending price. Now,
plot the results from the table on a line and imagine doing it for all
prices in-between…
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option
We have a graph for the payoffs from buying the stock outright. The
graph is often to use to understand the payoffs for derivatives.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option
We see that this investment has large potential gains and losses.
However, by using options we could minimize the losses. If this was
your intention, then should you purchase a “Call” or “Put” option?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Put Option
Suppose you purchased a Put Option at the same time you purchase
this stock. Recall, a put option will give you the right – but not
obligation – to sell the stock at the exercise price.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Put Option
Suppose the put costs you $5 and has an exercise price of $50. First,
how would you graphically describe the profit and loss from the put
option by itself? Hence, ignore the fact that you purchased the stock
for now.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Put Option
If the price at the end of the three months fell to near zero, then you
could exercise your option and purchase the stock at near zero, then
sell it for $50 – making a nice profit of $45 (the $50 sale price minus the
cost of the option).
Profit and Loss
+45
0
Price
40
45
50
55
60
Stock Option: Put Option
If the price falls only to $45, then you would just break-even. Thus, you
purchase the stock for $45 and sell it immediately for $50 making $5,
but that was the cost of the option itself.
Profit and Loss
+45
0
Price
40
45
50
55
60
Stock Option: Put Option
If the price rose to say $60, then you would not exercise the option.
Because if you did, you would have to pay $60 for a stock that you’ll
sale for $50. The nice thing about the “option” is that you need not use
it. Thus, you end up losing the $5 that it cost you to buy the option.
Profit and Loss
+45
0
-5
Price
40
45
50
55
60
Stock Option: Put Option
We can now plot the profit and loss opportunities from purchasing the
$5 put. Buying a put option along would be an indication that you were
very ‘bearish’ on this stock – believing its price will fall within the next
three months.
Profit and Loss
+45
0
-5
Price
40
45
50
55
60
Stock Option: Put Option
Notice why options are so tempting to speculators. You only need to
have the cost of the option in order to ‘bet’ on the price of this stock.
Profit and Loss
+45
0
-5
Price
40
45
50
55
60
Stock Option: Put Option
Now, return to our initial purchase of the IBM stock. Our intention was
to purchase the stock and attempt to reduce our risk of big losses.
Thus, we purchase the $5 put option at the same time. How will our
profits and loss opportunities change?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Put Option
If the price ends up below $50, then we can exercise our option to sell
the stock at a price of $50 – resulting in a $5 loss (don’t forget about
the cost of the option).
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Put Option
If the price ends up at $55, then we do not exercise our option to sell at
$50. We break-even in this case: Sell stock at $55 making $5 ($55$50) which just covers the cost of the option.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Put Option
At any price above $55, we will make a profit. The profit will always be
$5 less than if we had simply bought the stock without the put option.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Call Option
Now, we will see how a call option is used. Suppose three months had
passed and the price of your stock remained at $50. You are forced to
sell in order to pay tuition (or, for whatever reason), but still remain
‘bullish’ on this stock – believing the price is about to skyrocket.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Call Option
You don’t want to miss out on the increase in the price which you
believe will occur soon. So, you take $5 from your sale and purchase a
“Call Option”. Recall, a call option gives you the right – but not
obligation – to buy an asset at the exercise price.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Call Option
The cost of the call option is $5 with an exercise price of $50, and an
expiration date 3 months from now. What are your profit and loss
opportunities? If the price in 3 months was below $50, what would
occur?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Call Option
If the price in 3 months was below $50, what would occur? You would
not exercise your right to buy the stock at $50 if the price at the time
was below it. Thus, you would lose the cost of the option. If the price
were between $50 and $55?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Call Option
If the price were between $50 and $55? Say the price ended up at
$53, then you would exercise your right to buy at $50, then immediately
sell at $53 – making $3. However, the option cost you $5, so you end
up losing $2. When the price rises above $55?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Call Option
When the price rises above $55? Say the price ended at $60, then you
exercise your option to buy at $50 and immediately sell at $60 –
making $10. After subtracting the cost of the option ($5), you end up
with a $5. How does this compare to simply buying the stock?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Call Option
For a $5 investment (the cost of the option), you have the opportunity to
make large profits. Compared to simply buying the stock (or, in this
example continuing to hold on to it and not pay tuition), your profit
opportunities are always $5 less with the call option. However, …
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Call Option
you can only lose the $5 cost of the option. The graph below is
identical to the situation of buying the stock and a $5 put option. These
will always be similar outcomes – though our numbers make them
identical.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
One last example might be useful. Suppose you had initially purchased
the stock at $50 and instead of buying a put option, had sold a call
option?
Stock Option: Selling a Call Option
One last example might be useful. Suppose you had initially purchased
the stock at $50 and instead of buying a put option, had sold a call
option?
By selling a call option, someone else may call upon you to sell your
stock to them. After all, in the previous example when you bought a
call option – you purchased the right to buy an asset at the exercise
price from someone. Now, the someone will be you. In essence,
someone will have the right to buy the stock from you at the exercise
price. The upside is that you will receive the cost of the option!
Stock Option: Selling a Call Option
As long as the price remains below $50, nobody will force you to sell
them the stock at $50 which they can purchase for less than that.
Hence, you get to pocket the $5 cost of the option. What happens
when the price is $55?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
If the price after 3 months is $55, then someone will call upon you to
sell them the stock for $50. You will need to purchase the stock at $55,
then sell it to them for $50 – losing $5. But, the loss is exactly balanced
by what you received for selling the option ($5). If the price goes
beyond $55?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
If the price should rise above $55, then you will begin making losses.
Say the price was $60. You will need to purchase the stock at $60 and
sell at $50, making a $10 loss which the cost of the option ($5) you
received does not cover. The situation grows worse as the price rises.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
Return to the case where you initially purchased the stock at $50. At
the same time, suppose you sell the call option. Below, we have how
each looks when done along. How will things look when we do both at
the same time?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
If the stock ends up below $50, then the call option we sold will not be
exercised. We will suffer losses on the stock we purchased, but the
losses will not be as severe – by the amount of the $5 received from
selling the call option.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
For example, if the price had ended up at $45, then we lose $5 on our
initial purchase of the stock at $50, but make up the loss from the sale
of the call option at $5. Hence, we break even. What if the price ends
at $50?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
If the price ends at $50, the option will not get exercised (why would
someone buy from us at $50 when the current market price is $50).
We make nothing on our initial purchase of the stock, but do make a
profit of $5 from the sale of the call option. What happens if the price
rises to $60?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
If the price rose to $60, then the option will be exercised. You will be
forced to sell our stock at the $50 exercise price (rather than the market
price of $60). However, we will still make $5 from the sale of the call
option. This would occur for any price above $50.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
Compare outcomes from (1) buying the stock – blue line - and (2)
buying the stock and selling a call option – red line. Why do the second
choice?
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option: Selling a Call Option
If you believed the stock price would not fluctuate very much (in this
case within a $10 range), then buying the stock and selling the call
option would be more profitable.
Profit and Loss
+10
+5
0
-5
-10
Price
40
45
50
55
60
Stock Option
The analysis of stock options carries over directly to options in futures.
We have only scratched the surface of how options and, more
generally, derivatives are used. Hopefully, you have seen how they can
be used to reduce risk. Also, you have seen why they are so tempting
as a tool of speculation. We have not covered how one might value
options. Of course, the market price of an option is determined like any
other financial asset by the forces of supply and demand. When we
talk about ‘valuing’ an option, we are interested in understanding the
determination of its ‘intrinsic value’. The famous Black-Scholes pricing
formula has played a dominate role in valuing options. This role has
been extending as more assets (both financial and real) become
conceptualized as options.