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.

c) Construct a delta-hedge position on January 4, 2016 involving the sale of 1,000 calls. Then rebalance the portfolio at the end of the next day, when the share price goes down to $135 per share. Assume the market call price is correct. That is, use the implied volatility as the correct volatility for the IBM shares. (You may calculate the deltas using the formula or the BlackScholesMertonBinomial10e.xlsm file provided by the textbooks authors. If you use the latter, include a screen shot of the Excel spreadsheet in your answer.)

Obtain the value of this delta-hedge 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. (12 marks)