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. 5. There is another call option on IBM shares with an exercise price of $125 and the same expiration date (March 18, 2016). Construct a delta- and gamma-hedge portfolio on January 4, 2016 involving the sale of 1,000 of the 130-call option. Then rebalance the portfolio at the end of the next day, when the share price goes down to $135 per share. Again, use the implied volatility as the correct volatility for the IBM shares.
Risk A1 Q5-5
Question 5. Volatility and Option Hedging
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.
5. There is another call option on IBM shares with an exercise price of $125 and the same expiration date (March 18, 2016). Construct a delta- and gamma-hedge portfolio on January 4, 2016 involving the sale of 1,000 of the 130-call option. Then rebalance the portfolio at the end of the next day, when the share price goes down to $135 per share. Again, use the implied volatility as the correct volatility for the IBM shares.
Step by step
Solved in 2 steps
