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FRL 367, Winter 2013 prepared by Dr. Ekaterina Chernobai Homework Assignment 4 "Black-Scholes Option Pricing Model" Terms of the homework: ~...

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1.annual risk-free rate
2. σ2annual
3. Problem 1
4. Problem 2

FRL 367, Winter 2013 prepared by Dr. Ekaterina Chernobai Terms of the homework: ~ Expiration date : Thursday, March 14. ~ The homework is an American option , which means you can exercise it on or prior to the expiration date. ~ Value at expiration : when homework is exercised: 30 points minus points lost when homework is not exercised: 0 points ( Make sure you realize that this homework is not optional! You must turn it in, otherwise your score for homework #4 is 0 points! ) Additional information: You can work on this homework alone or with one other student in class. If you work with one other student, please turn in just one set of solutions with both names on it – both will receive the same grade. Half of the score for each problem is based on your write-up , i.e., an explanation of what you are calculating in each step and why – for full credit show all calculations (i.e., formulas used, numbers that go into the formulas, or what you plug into your financial calculator) and briefly explain in words why you are doing what you are doing with each step of your calculations . To turn in your homework solutions: o Type your solutions in Word document (.doc file). o Email to me this Word document file by the beginning of March 14 lecture. The solutions will not be graded until I’ve received the electronic version. If you work with one other student, please indicate both partners’ names in the email. o FORMATS OTHER THAN “WORD” DOCUMENT – such as Excel spreadsheets or printscreens thereof – WILL NOT BE ACCEPTED. (I will not be clicking on the cells of your spreadsheets to check where the numbers came from.) If you did part of your work in Excel you can create a table in your Word document & add a write-up which clearly explains where all new numbers in your table come from (see 2 nd bullet point above). o Print out the same Word document file with your solutions and turn this hard copy in to me by the beginning of March 14 lecture. The hard copy should be identical to the emailed solutions. Feel free to email to me your questions on the homework or ask those during office hours Homework Assignment 4 “Black-Scholes Option Pricing Model”
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The idea of this homework is very simple: use the Black-Scholes option pricing formula to check whether a call option is priced correctly. - Pick any company of your choice, whose stock is traded on NYSE (New York Stock Exchange) and which has options written on it. - There are different websites which give details about companies’ options. Here’s one that you can refer to: . Go to “Investing” tab on top. - On that website, if you go to “Markets” and then “Treasurys”, you can find the annualized yield (rate of return) on US Government Treasury bills. The three-month one is the one that is most commonly used to determine the annual risk-free rate. (You can read up more on how to interpret US Treasury bill quotes on the New York Fed’s website: ) - On the same website, if you go to “Stocks” tab and type in the correct symbol for the company that you have chosen, you can see information on call options, put options, and other current information on the stock. - Choose any month you like for the option expiration month. Choose any exercise price you like for which the option is in-the-money. The column labeled “Ask” shows the current price at which call options with different exercise prices can be purchased. - As part of your calculations you will need to calculate σ 2 , which in the Black-Scholes formula is variance (per year) of the continuous returns on stock. This is the expected stock return volatility between the purchase date and the expiration date. Unfortunately, this represents the future, so there is no way you can know the correct volatility. What traders do instead is estimate this volatility using past data. I would like you to calculate stock return volatility using daily stock prices (closing prices) for the last 3 months (90 last trading days) of stock trading. allows you to download a spreadsheet with historical stock prices. You would need to select “daily”. To convert the resulting daily return volatility into the annual volatility, use the following formula: σ 2 annual = σ 2 daily x (total number of trading days in 2013) Based on the information above, answer the following questions (see next page): 2
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