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Project 3 - Introduction

Project 3 - Introduction. Pricing a Stock Option . Pricing a Stock Option . Our goal is to determine a fair price for a stock option. This is also known as the premium for the option. Example.

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Project 3 - Introduction

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  1. Project 3 - Introduction Pricing a Stock Option

  2. Pricing a Stock Option • Our goal is to determine a fair price for a stock option. This is also known as the premium for the option.

  3. Example IBM is now selling for $120 per share. Suppose you believe that the stock will be selling for $140 per share by the third week of next March. Option costs $10 per share. Two choices: to buy a stock? or to buy a stock option? What is the difference?

  4. What is a stock option? Stock option gives the owner the right, but not the obligation, to buy or sell the stock for a pre-specified price (called the strike price or exercise price) , over a specified period of time.

  5. Going back to the example If you buy a share of IBM stock now for $120 and hold it until March, you expect to sell the share for $140, realizing a net income of $20. Ignoring potential for interest, this is a return of $20/$120 or 16.7% on your investment.

  6. Alternative: stock option Use the $120 to buy an IBM call option for twelve shares (suppose a call option costs $10 per share), with a strike price of $125. By next March, you expect to be able to buy 12 shares of IBM for $125 each and then immediately sell them at the market price of $140.

  7. Your income would be 12 shares * $15 ($140-$125) = $180. Since you paid $120 for the option, your net profit is $180-$120= $60. This is a return of $60/$120 = 50% on your $120 investment. If IBM share is indeed going to be $140 in March, a call option is a smarter choice over stock

  8. Call option: is a right to buy a stock Put option: is a right to sell a stock. Strike price: is the pre-specified price at which the option holder may buy (in case of a call) or sell (in case of a put).

  9. American option: may be exercised at any time prior to its expiration. European option: may only be exercised on its expiration date.

  10. Duration or Period Options are described by the number of weeks or months from the time of purchase until the end of the period, at which the strike price may be used. If period is given in weeks, it is assumed to end on Friday of the given week. For months, it ends on the 3rd Friday of that month.

  11. Example A European call option on IBM, with a strike price of $125 and an expiration of next March allows a person to buy IBM shares for $125 on the 3rd Friday of next March.

  12. This option is worthless if IBM sells for less than $125 by next March. The holder loses all of the money paid for the option. On the other hand, if IBM is selling for $135 on the expiration date, the owner can exercise the option, buy shares at $125, and immediately sell them for $135 with an income of $10 per share.

  13. The Value of a Call Option • How do you calculate the value of a call option? • Let C be price of a share of stock at the end of an option period and S be the strike price. Then:

  14. Going back to the IBM example Suppose you purchased a call to buy shares at $125 and the actual price is $124 by next March. So the call option is worthless and you lose all of your original $120 in buying the option for $10 per share. In this case, it is better to buy the stock than the stock option.

  15. Example You purchased the option to buy Boeing stock with a strike price of $30. Find the value of the option, if the price of the stock is: $29.50 per share (0) $32.75 per share (2.75)

  16. example You paid $2.95 for the option to buy Boeing stock with a strike price of $30. Find your overall profit (or loss), if the price of the stock at the end of the option period is: $29.50 per share (-2.95) $33.05 per share (0.10)

  17. Example You have $400 to invest. Currently a stock costs $80 per share. A call option with a strike price of $85 costs $5 per share. Three months later, the stock drops to $65. Find the profit made from • Buying 5 shares of stock (-$75) • Buying 80 shares of a call option (-$400)

  18. Options are bought and sold in open markets, as much the same way that stocks are traded. Trading options is a very important part of modern finance. The problem of determining the present value of an option is one of considerable interest.

  19. Note of Caution Investing in options or stock market is unpredictable business and depends on many factors. This project is a very simplified form and does not in any way guarantee anyone to become expert stock buyers or sellers.

  20. Assumptions for option pricing: 1. Past history cannot be used to predict the future price of a stock. If this could be done, all investors would move their money to the stock with the best-predicted return. This would drive up the price of that stock, destroying its potential value.

  21. 2. Past history of prices for a given stock can be used to predict the amount of future variation in the price of the stock. Market history shows stocks whose price has fluctuated widely in the past will continue to fluctuate; those with limited variability will retain that trait. The extent of a stock price’s variability is called its volatility.

  22. 3. All investments are assumed to give the same rate of return. If this were not so, then all smart investors would switch their money to the investment with the highest predicted rate of return. This would raise the cost of the chosen investment and destroy its predicted rate of return.

  23. 4. We will assume that the common growth rate mentioned in assumption 3 is the same as the rate of return on a U.S. Treasury Bill. Since the federal government guarantees the rate of this investment, it is called the risk-free rate.

  24. 5. All investments with the same expected rate of growth are considered to be of equal value to investors. Obviously, some people will prefer one type of investment over another. However, tastes will vary, so we will ignore it in our pricing. This is called the risk neutral assumption.

  25. 6. The stock does not pay dividends, and commissions are not charged for purchasing the option. While in real life, the opposite is normally true. Dividends and commissions vary so much that we will not consider them in pricing the option.

  26. 7. The option is a European call option.

  27. Class Project 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, with a strike price of $23. Our work is to be based upon the weekly closing of stock’s price record for the past 8 years.

  28. Class Project In practice, both a bid (what someone is willing to pay) and an asked price (at which someone is willing to sell) are quoted for options. To simplify things, we will assume that these are the same.

  29. Class Project Walt Disney trades on the NY Stock Exchange under the ticker symbol DIS. Information downloaded on January 11, 2002 is shown in the excel file Option Data.xls. Relevant data have been copied into the data sheet of the file.

  30. Class Project One important fact is that Walt Disney closed at an actual value of $21.87 on January 11, 2002. We can use our historical data to gather information on volatility, as discussed in Assumption 2. Calculation: What is the % change for the most recent pair of weekly data in the file?

  31. Class Project Finally, we will suppose that on January 11, 2002, the annual interest rate for a 20 week U.S. Treasury Bill was 4% compounded continuously. This will be used as the risk-free rate, which is discussed in Assumption 4.

  32. Class Project Our ONLY GOAL is to determine a fair option price. We have no interest in whether or not people should have bought such an option, or even whether or not they should have bought Disney stock. We also have no interest in predicting the closing value of Disney stock at the expiration of the option.

  33. Team Projects Go to class website in “link to files”. Double click on “Project 3 Team data”. Each team is given:

  34. Each team should have: -the name and ticker symbol of your team stock. -the starting date of your stock option. -the number of weeks for which its option is to run. -the number of years of historical data that will be used in pricing your option. -strike price. -starting data risk-free interest rate of a treasury bill for the same period as your stock option.

  35. Your team is going to use the methods we will discuss in class to determine the value per share, at the option’s starting data, of a European call on its stock. To get 3 years of historical data in your company’s stock prices, go to Yahoo.com>Finance and type in the ticker symbol. Select historical prices for 3 years starting February 1, 2007 and select weekly. We just need the date, week# and the adjusted closing prices.

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