Question
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
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 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.
e) e. Explain the difference between the delta-hedged portfolio value in part (c) and the delta-and-gamma-hedged portfolio value in part (d). (1 mark)
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