Reference no: EM132952685

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

Januay                 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 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.

Problem a. 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).

Problem b. Based on the market price of $6.50, derive the implied volatility on the IBM shares. You may use the Black Scholes Merton Implied Volatility 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).