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Posted By View Student Profile

Subject Business

Deadline (Pacific Time) 04/30/2017 12:00 am

Budget $10-$30

Students are asked to estimate stock (return) volatility using two methods � the historical data approach and BSM implied volatility approach, and then compare the two estimates. The historical volatility requires historical data and is used to predict the future volatility. The BSM implied volatility gives more accurate prediction of the current volatility of the underlying stock especially when the market changes significantly. The project aims to help students understand the two volatility measures as well as the BSM model. Project instruction: Note: the instruction omits some details in calculating sample variances and standard deviation. You may need to use your Statistics class notes / textbooks. Step 1. Choose a stock and a related option Choose a public firm�s common stock that also satisfy criteria such as: No dividend � because the basic BSM model assumes no dividend payments. Well-known firm � for better data availability Have at least one year historical daily return available for use. Options are traded recently and have trading price available. The option should be a call option written on the stock. Select the strike and maturity, at your discretion. Step 2. Download market data You need the data items as below: Historical daily stock prices. There are plenty of financial websites that offer free historical stock price download. To search for the financial websites, use key words such as �historical stock price download�. Recent option trading data � the last price, strike, and maturity date. Step 3. Find the proper risk free rate Find the risk free rate that best matches the option�s maturity. For instance, if the call option matures in one year, then you need to find the yield on the T-bills that expires in one year (find more information in your Business Finance course textbook/notes). If you are not able to find a exact match of the maturities, find the closest one. Step 4. Calculate historical volatility Calculate daily return. Use: (P1-P0)/P0 Calculate continuously compounding daily return. Use: ln (1 + daily return) Calculate sample variance of the continuously compounding daily return 1 – 1 ?( – ̅) 2 =1 Calculate standard deviation of the continuously compounding return. It is the square root of the sample variance. Step 4. Calculate implied volatility Use the implied volatility spread sheet named �BSMImpVol9e.xls� to find implied standard deviation of the stock returns. For best results, the stock price S and the last price for option C should be for the same trading day. Step 5. Complete a short (!!!) project report. Your report should NOT exceed two pages and should include the three sections/paragraphs: 1. Description of your estimating process. Include variables and parameters used in your project, necessary assumptions, difficulties met in data collection and calculation. 2. Compare the values of the two volatility measures. Explain what may have contributed to the difference. 3. References. In your report, make sure to include all data sources, date on which the data were obtained, web sites used, etc. Report format: Use Times New Roman font, size 12, double space, and no space before or after each paragraph for the entire document. Use the �Justify� option to align the text. Section titles are optional.