Question 5. Volatility and Option Hedging (34 marks) Today, is January 4, 2016. IBM common stock is selling at $135.95 per share. The stock has a dividend yield of 4% per year. The following table contains the monthly stock prices for IBM shares during the last 12 months. Month (2015) IBM Share Price January 148.46 February 157.92 March 156.51 April 167.04 May 166.69 June 159.82 July 159.16 August 146.52 September 143.62 October 138.78 November 139.42 December 137.62 a. A call option with a March 18, 2016 expiration date and an exercise price of $130 is currently trading at $6.50. Each option entitles the holder to purchase 100 IBM shares. The risk-free rate is 0.58%, compounded continuously. Shares and options can only be bought and sold in whole numbers. Note that 2016 is a leap year. Compute the historical volatility in terms of annualized standard deviation on the IBM shares, using the 12-month price data in the table above. Note that the volatility should be calculated on the stock returns and not on the stock prices. Obtain your answer to four decimal places (or two decimal places in percentage). (3 marks) b. Based on the market price of $6.50, derive the implied volatility on the IBM shares. You may use the BlackScholes MertonImpliedVolatility10e.xlsm file provided by the textbook's authors to derive the implied volatility. Take a screen shot of the answer provided in this Excel spreadsheet, and copy and paste it into your answer for this question. Obtain your answer to four decimal places (or two decimal places in percentage). (2 marks) Question 5. Volatility and Option Hedging (34 marks) Today, is January 4, 2016. IBM common stock is selling at $135.95 per share. The stock has a dividend yield of 4% per year. The following table contains the monthly stock prices for IBM shares during the last 12 months. Month (2015) IBM Share Price January 148.46 February 157.92 March 156.51 April 167.04 May 166.69 June 159.82 July 159.16 August 146.52 September 143.62 October 138.78 November 139.42 December 137.62 a. A call option with a March 18, 2016 expiration date and an exercise price of $130 is currently trading at $6.50. Each option entitles the holder to purchase 100 IBM shares. The risk-free rate is 0.58%, compounded continuously. Shares and options can only be bought and sold in whole numbers. Note that 2016 is a leap year. Compute the historical volatility in terms of annualized standard deviation on the IBM shares, using the 12-month price data in the table above. Note that the volatility should be calculated on the stock returns and not on the stock prices. Obtain your answer to four decimal places (or two decimal places in percentage). (3 marks) b. Based on the market price of $6.50, derive the implied volatility on the IBM shares. You may use the BlackScholes MertonImpliedVolatility10e.xlsm file provided by the textbook's authors to derive the implied volatility. Take a screen shot of the answer provided in this Excel spreadsheet, and copy and paste it into your answer for this question. Obtain your answer to four decimal places (or two decimal places in percentage). (2 marks)
