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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