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. 6. Obtain the value of this delta-and-gamma-hedged portfolio after it has been rebalanced. Compare this value to the target value of the portfolio should its initial value be invested at the risk-free rate. Explain the difference.
Risk A1 Q5-6
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.
6. Obtain the value of this delta-and-gamma-hedged portfolio after it has been rebalanced. Compare this value to the target value of the portfolio should its initial value be invested at the risk-free rate. Explain the difference.
Step by step
Solved in 2 steps
