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)