Chapter 19
Options
http://www.youtube.com/watch?v=cOReCqIMu2s
Nobel Prize in Economics
• 1997 7,500,000SEK (1,231,601
CAD)
Robert Merton and Myron Scholes
“For a New Method to Determine the
Value of Derivatives”
Long-Term Capital Management On its
board of directors were Myron Scholes
and Robert C. Merton in 1998 it lost
$4.6 billion in less than four months
Learning Objectives
• Define options and discuss why they
are used.
• Describe how options work and give
some basic strategies.
• Explain the valuation of options.
• Identify types of options other than
puts and calls.
Payoff Diagram for a Call
Option
Profit per
Option ($)
Buyer
4
0
25
27
29
Stock Price
at Expiration
-4
Seller
How does buying a stock compare
with buying a call option?
Payoff Diagram for a Put
Option
Profit per
Option ($)
4
Buyer
0
23
-4
25
27
Stock Price
at Expiration
Seller
How does selling a stock compare
with buying a put option?
Covered Call Writing
Profit ($)
Purchased
share
Combined
4
0
23
-4
25
27
29
Stock Price
at Expiration
Written call
Protective Put Buying
Profit ($)
Purchased
share
Combined
4
0
23
-4
25
27
29
Stock Price
at Expiration
Purchased
put
Portfolio Insurance
• Hedging strategy that provides a
minimum return on the portfolio while
keeping upside potential
• Buy protective put that provides the
minimum return
–
Put exercise price greater or less than
the current portfolio value?
• Problems in matching risk with
contracts
Portfolio Insurance
Profit ($)
Purchased
share
Combined
2
0
23
25
27
29
Stock Price
at Expiration
-2
Purchased
put
Should Options be Exercised
Early?
• Exercise prior to maturity implies the
option owner receives intrinsic value
only, not time value
–
For call options, buy stock at below market
price
•
–
Would more be earned by selling option?
For put options, receive cash from selling stock
at above market price
•
Could cash be reinvested for a higher return?
Option premiums
=Intrinsic+Time
• At maturity, option prices are equal
to their intrinsic values
–
Intrinsic value is minimum price prior to
maturity
• Maximum option prices prior to
maturity
–
–
Call options: S
Put options: K
Black-Scholes Model
The Black-Scholes pricing formula is:
C  SN (d1 )  Ke  RT N (d 2 )
where
d1 
S
ln 
K
2
 
   R 
2
 
 T
and
d 2  d1   T

T

Put-Call Parity
Profit ($)
Purchased
share
Combined
4
0
23
-4
25
27
29
Stock Price
at Expiration
Written call
Factors Affecting Prices
Variable
Stock Price
Exercise Price
Time to maturity
Stock volatility
Interest rates
Cash dividends
Call
+
+
+
+
-
Put
+
+
+
+
Hedge Ratios
• Options can be used to control the
riskiness of common stocks
–
If stock owned, sell calls or buy puts
• Call or put option prices do not usually
change the same dollar amount as the
stock being hedged
–
–
Shares purchased per call written = N(d1)
Shares purchased per put purchased = N(d1)
-1
Other Types of Options
• Stock-Index Options: option
contracts on a stock market index
• Interest Rate Options: option
contracts on fixed income securities
• Currency Options: Option contracts
whose value is based on the value of
an underlying currency