Question 4. (a) Reload Options. Reload options are often issued to ex- ecutives as part of their compensation packages. They are American-style options, giving the holder the option to exercise at any time and take up now at-the money options. Thus, suppose an option with a strike price of K has 7 years of life remaining, and the current stock price S, is greater than K, so immediate exercise is indicated. On exercise, the executive receives an amount S, - K in cash plus a number K/5, of at-the money options with time to maturity T-1. Reload options can be valued using a binomial tree. Suppose, for a non- dividend paying stock, So = 100, K = 100, g - 0.3, r - 0.08, and T = 4. Set up and use a 2-step binomial tree to value (i) an ordinary American option: 2 marks (ii) a reload option, with these parameters. [6 marks (b) Housing Equity Finance Loan. A lender offers the following deal. At Time 0, borrow up to 20% of the value of a house, interest free. At Time T, repay principal plus 40% of any capital gain OR repay principal minus 20% of any capital loss. (1) Write a formula for the value ca of the option at Time 0, defining all quantities and stating any assumptions. 13 marks (ii) Find co when 7 = 25 years, r = 5% p.a., o = 10% p.a. (1 mark] (iii) Obviously you must pay more for the option component. How much more? Express your answer as effective extra interest paid on the loan, and comment. 12 marks SEE OVER