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Project 2: Stock Option Pricing 1 Project 2: Stock Option Pricing 1

Business Background • Bonds & Stocks – to raise Capital • When a company 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 2

Stock Option • A derivative security • Value derived from the underlying stock • 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 3

Options Vs. Stocks • Similarities • Listed options are securities, just like stocks • 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 4

Strike Price (S) • The price specified in the option contract • The per 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 5

Expiration date • The date on which the option contract expires – In the 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) 6

Closing Stock price (C) • The stock price on the day we decide to 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 7

Types of Options • Call Option - gives the holder(buyer) the right to BUY 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 8

Exercise Buyers invoke their rights • Call Exercise: Call buyers choose to buy stock 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) 9

When do we exercise Options? • Call options closing stock price > strike price When do we exercise Options? • Call options closing stock price > strike price • Put options closing stock price < strike price 10

Example 1 • An American call option • Since it is a CALL option 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 11

Example 1 Let us consider two cases STRIKE PRICE - $15. 00 May 2, Example 1 Let us consider two cases STRIKE PRICE - $15. 00 May 2, 2003 July 18 th, 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 12

Example 1 • If case 1 occurs- the holder will benefit by exercising the Example 1 • 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 13

Example 1 Final value of Call option (Intrinsic Value of a Call) Maximum of Example 1 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 14

Example 1 Final value of Call option July 18 th, 2003 STRIKE PRICE - Example 1 Final value of Call option July 18 th, 2003 STRIKE PRICE - $15. 00 Case 1 Stock- $20. 00 Call- $5. 00 May 2, 2003 Stock- $13. 45 Call- $0. 45 Case 2 Maximum of 0 and C-S Max(0, -5)=0 Maximum of 0 and C-S Max(0, 5)= 5 Stock- $10. 00 Call- $0. 00 Recall : Call option exercise criteria: if closing stock price > strike price 15

Example 1 Analysis of Case 1 & Case 2 • Case 1(closing stock price Example 1 Analysis of Case 1 & Case 2 • 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. 45 X 100=$45 (Excluding transaction cost) 16

Example 2 • An American put option • Since it is a PUT option 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 17

Example 2 Let us consider two cases STRIKE PRICE - $10. 00 May 2, Example 2 Let us consider two cases STRIKE PRICE - $10. 00 May 2, 2003 July 18 th, 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 18

Example 2 • If case 1 occurs- the holder will not benefit by exercising 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 19

Example 2 Final value of Put option (Intrinsic Value of a Put) Maximum of 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 20

Example 2 -Final value of Put option July 18 th, 2003 STRIKE PRICE - Example 2 -Final value of Put option July 18 th, 2003 STRIKE PRICE - $10. 00 Case 1 Stock- $15. 00 Put- $0. 00 May 2, 2003 Stock- $13. 45 Put- $0. 15 Case 2 Maximum of 0 and S-C Max(0, 5)=5 Maximum of 0 and S-C Max(0, -5)= 0 Stock- $5. 00 Put- $5. 00 Recall : Put option exercise criteria: if closing stock price< strike price 21

Example 2 Analysis of Case 1 & Case 2 • Case 1 closing stock Example 2 Analysis of Case 1 & Case 2 • 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. 15 X 100=$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 22

The In’s and Out’s of Options In-The-Money Calls: • Stock price is above strike 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. 23

The In’s and Out’s of Options Out-of-The-Money Calls • Stock price below strike price 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. 24

The In’s and Out’s of Options At-The-Money Calls: • Stock price equal to strike 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. 25

Volatility • A measure of risk • Volatility is the extent of a stock Volatility • A measure of risk • Volatility is the extent of a stock price’s variability 26

Risk-free rate • We will assume that the common growth rate for all investments 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 27

Project 2 -Goal • To find the present value, per share, of a European 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 28

Class Project We suppose that it is Friday, January 11, 2002. Our goal is 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) 29

Preliminary Reports – Project 2 Required components • the goal of the project To 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 30

Preliminary Reports – Project 2 • Discuss the specifics of your option contract • 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 part 1. 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 31