The current price price of the share is $10 and may in one time-step go either up to $12 or down to $8. The strike price of a call option is $11.50. Assume an annual interest rate of 2.6%, and a time of 12 months to the exercise date. (a) Calculate the value of the call option using the one step binomial model. Show all working. (7 marks) (b) Suppose you have just sold 6000 of the call options to a dealer for $0.35 each. Determine how many shares you should you buy or sell in order to hedge your risk (i.e. so there is no risk) and find your profit when the share price increases and when it decreases. (8 marks) (c) Next calculate the value of the call option using a multistep binomial model with one step per fortnight. Adjust the interest rate and increments so that the "volatility" is approximately the same. (6 marks) (d) Repeat the calculation in (c) with a multistep model with twice as many steps, appropriately adjusting the parameters. (4 marks) (e) Compare the option values in (a), (c), (d) and draw conclusions. (2 marks)