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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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Example1Let us consider two cases
Stock- $13.45
Call- $0.45
Stock- $20.00
Stock- $10.00
July 18th, 2003
May 2, 2003
Recall :Call option exercise criteria: if closing stock price > strike price
Case 1
Case 2
STRIKE PRICE - $15.00
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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
Stock- $13.45
Call- $0.45
Stock- $20.00Call- $5.00
Stock- $10.00Call- $0.00
July 18th, 2003
May 2, 2003
Recall :Call option exercise criteria: if closing stock price > strike price
Maximum of 0 and C-SMax(0,5)= 5
Maximum of 0 and C-SMax(0,-5)=0
Case 1
Case 2
STRIKE PRICE - $15.00
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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 exercisedWhat are the cost ? Initial price paid for the contractTotal 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
Stock- $13.45
Put- $0.15
Stock- $15.00
Stock- $5.00
July 18th, 2003
May 2, 2003
Recall :Put option exercise criteria: if closing stock price < strike price
Case 1
Case 2
STRIKE PRICE - $10.00
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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
Stock- $13.45
Put- $0.15
Stock- $15.00Put- $0.00
Stock- $5.00Put- $5.00
July 18th, 2003
May 2, 2003
Recall :Put option exercise criteria: if closing stock price< strike price
Maximum of 0 and S-CMax(0,-5)= 0
Maximum of 0 and S-CMax(0,5)=5
Case 1
Case 2
STRIKE PRICE - $10.00
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Example 2 Analysis of Case 1 & Case2
• Case 1 closing stock price > strike price the put option would not be exercisedWhat are the cost ? Initial price paid for the contractTotal 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-the-money. 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-of-the-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-the-money.
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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 ProjectWe 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 2Required 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