Project 2: Stock Option Pricing
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Business Background
• Bonds & Stocks – to raise Capital
• When a company sell a Bond
- borrows money from the investor
- pays interest regularly
- repays the money on maturity date
• When a company issues stock
-sells the ownership position in the company
-shareholder’s equity=Assets-Liabilities
-earnings distributed in form of dividends
-stock sold at exchanges. e.g. NYSE, CSE
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Stock Option
• A derivative security
• Value derived from the underlying stock
• Stock option
- A contract that gives the holder (buyer) of the option
the right to buy or sell 100 shares the underlying stock
on or before a specified date
-holder (buyer) is not obligated to exercise the option
-writer (seller) is obligated to honor the terms of the
contract if the option is exercised
- strike (exercise) price is the price specified in the
contract
- expiration date
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Options Vs. Stocks
• Similarities
• Listed options are
securities, just like
stocks
• Options trade like
stocks
• Options are actively
traded in a listed
market, just like
stocks
• Differences
• Options are
derivatives,unlike stocks
• Options have expiration
dates,while stocks do not
• There is not a fixed number
of options, as there are with
stock shares available
• Stockowners have a share of
the company with voting and
dividend rights. Options
convey no such rights
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Strike Price (S)
•
The price specified in the option
contract
•
The per share price at which the
underlying stock can be bought or sold
under the terms of the option contract
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Expiration date
• The date on which the option contract
expires – In the U.S the expiration date is
usually the THIRD FRIDAY of the month
-American option (can be exercised prior to
expiration date)
-European option ( can be exercised only on
the expiration date)
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Closing Stock price (C)
• The stock price on the day we decide to
exercise the option contract
• The closing stock price is important to
make the decision
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Types of Options
• Call Option
- gives the holder(buyer) the right to BUY
the underlying stock
• Put Option
- gives the holder(buyer) the right to SELL
the underlying stock
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Exercise
Buyers invoke their rights
• Call Exercise: Call buyers choose to buy
stock at the strike price
(from the call seller)
• Put Exercise: Put buyers choose to sell
stock at the strike price
(to the put seller)
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When do we exercise Options?
• Call options closing stock price > strike price
• Put options
closing stock price < strike price
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Example 1
• An American call option
• Since it is a CALL option the holder has
the right to BUY stocks
• Given
-strike price $15.00
-expiration date July 18,2003
-the price of option $0.45 on May 2003
-either case 1 or case 2 can happen
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Example1
Let us consider two cases
STRIKE PRICE - $15.00
May 2, 2003
July 18th, 2003
Stock- $20.00
Case 1
Stock- $13.45
Call- $0.45
Case 2
Stock- $10.00
Recall :Call option exercise criteria: if closing stock price > strike price
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Example1
• If case 1 occurs- the holder will benefit by
exercising the option
• If case 2 occurs- the holder will not benefit
by exercising the option
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Example1
Final value of Call option (Intrinsic Value of a Call)
Maximum of 0 and C – S
• C – The price of the underlying stock on
the expiration date
• S – The strike price of a call option
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Example1
Final value of Call option
July 18th, 2003
STRIKE PRICE - $15.00
Case 1
Stock- $20.00
Call- $5.00
May 2, 2003
Maximum of 0 and C-S
Max(0,5)= 5
Stock- $13.45
Call- $0.45
Case 2
Maximum of 0 and C-S
Max(0,-5)=0
Stock- $10.00
Call- $0.00
Recall :Call option exercise criteria: if closing stock price > strike price
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Example1
Analysis of Case 1 & Case2
• Case 1(closing stock price > strike price)
Total Profit= [(closing price-strike price)-option price] X 100
=[(20.00-15.00)-0.45] X 100=$455.00
• Case 2
closing stock price < strike price
the call option would not be exercised
What are the cost ?
Initial price paid for the contract
Total cost=option price X 100=0.45X100=$45
(Excluding transaction cost)
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Example 2
• An American put option
• Since it is a PUT option the holder has the
right to SELL stocks
• Given
-strike price $10.00
-expiration date July 18,2003
-the price of option $0.15 on May 200
-either case 1 or case 2 can happen
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Example 2
Let us consider two cases
STRIKE PRICE - $10.00
May 2, 2003
July 18th, 2003
Stock- $15.00
Case 1
Stock- $13.45
Put- $0.15
Case 2
Stock- $5.00
Recall :Put option exercise criteria: if closing stock price < strike price
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Example 2
• If case 1 occurs- the holder will not benefit
by exercising the option
• If case 2 occurs- the holder will benefit by
exercising the option
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Example 2
Final value of Put option (Intrinsic Value of a Put)
Maximum of 0 and S-C
• C – The price of the underlying stock on
the expiration date
• S – The strike price of a Put option
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Example 2 -Final value of Put option
July 18th, 2003
STRIKE PRICE - $10.00
Case 1
Stock- $15.00
Put- $0.00
May 2, 2003
Maximum of 0 and S-C
Max(0,-5)= 0
Stock- $13.45
Put- $0.15
Case 2
Maximum of 0 and S-C
Max(0,5)=5
Stock- $5.00
Put- $5.00
Recall :Put option exercise criteria: if closing stock price< strike price
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Example 2
Analysis of Case 1 & Case2
• Case 1
closing stock price > strike price
the put option would not be exercised
What are the cost ?
Initial price paid for the contract
Total cost=option price X 100=0.15X100=$15
(Excluding transaction cost)
• Case 2(closing stock price < strike price)
Total Profit= [(strike price- closing price)-option price] X 100
=[(10.00-5.00)-0.15] X 100=$485.00
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The In’s and Out’s of Options
In-The-Money Calls:
• Stock price is above strike price
• In-the-money calls have intrinsic value
Example:
With a stock price of $63, the 60 Call is in-themoney. Specifically, it is in-the-money by $3,
and it has $3 (per share) of intrinsic value.
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The In’s and Out’s of Options
Out-of-The-Money Calls
• Stock price below strike price
• Out-of-the-money calls do not have intrinsic
value
Example:
With a stock price of $63, the 65 Call is out-ofthe-money. Specifically, it is out-of-the-money
by $2, and it has no intrinsic value.
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The In’s and Out’s of Options
At-The-Money Calls:
• Stock price equal to strike price
• At-the-money calls do not have intrinsic value
Example:
With a stock price of $60, the 60 Call is at-themoney.
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Volatility
• A measure of risk
• Volatility is the extent of a stock price’s
variability
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Risk-free rate
• We will assume that the common growth
rate for all investments whose future
values can be predicted is the rate of
return on a United States Treasury Bill.
• Since the rate for this investment is
guaranteed by the federal government,it is
called the risk free rate
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Project 2 -Goal
•
To find the present value, per share,
of a European call option of a particular stock,
unique to each team.
• The expiration, the strike price, and the
number of years of historical data will be given
to each team
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Class Project
We suppose that it is Friday, January 11, 2002.
Our goal is to find the present value, per
share, of a European call on Walt Disney
Company stock.
• The call is to expire 20 weeks later
• strike price of $23.
• stock’s price record of weekly closes for the
past 8 years(work basis).
• risk free rate 4% (this means that on Jan
11,2002 the annual interest rate for a 20 week
Treasury Bill was 4% compounded
continuously)
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Preliminary Reports – Project 2
Required components
• the goal of the project
To find the present value, per share,
of a European call option of a
particular stock, unique to each team.
• Give background on underlying security
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Preliminary Reports – Project 2
• Discuss the specifics of your option contract
• Definitions(Eg:
stock
options/call
option/put
option/American option)
• Show a sample of downloaded data(Must use yahoo
website/ More information & instructions on slide #69
of MBD part1.ppt)
• Create a graph in Excel of the closing prices for the
relevant years
(Randomly select a closing price for each year)
Eg: if you are analyzing 8 years you should have 8
closing prices)
• 5-6 minutes presentation
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