Delta hedging

Question 1 (20 Marks) You are writing call options on stock S. The current price of Sis 80. Over the next year the stock price will either increase by 20 percent (u=1.2) or decrease by 20 percent (d=0.8). That is, the price may be either 96 or 64. Assume that the bank can borrow and lend at the risk-free interest rate of 2.5% (annually compounded). The stock S does not pay dividends. You are selling 10.000 European call options on with a one year maturity and a strike price of 80. You dynamically hedge (delta hedge) your option position, Construct a one-stage binomial model to calculate: a) The number of shares of S you have to hold to hedge your option position. (8 marks) b) The break-even price for an option on S you are selling. (7 marks) c) The amount of money you will need to borrow now to establish the hedge