5. First Semester Examinations FINM3003 June, 2021 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 new at-the-money options. Thus, suppose an option with a strike price of K has T years of life remaining, and the current stock price St is greater than K, so immediate exercise is indicated. On exercise, the executive receives an amount St - K in cash plus a number K/S, of at-the-money options with time to maturity T - t. Reload options can be valued using a binomial tree. Suppose, for a non- dividend paying stock, So = 100, K = 100, o = 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. (i) Write a formula for the value co of the option at Time 0, defining all quantities and stating any assumptions. [3 marks] (ii) Find co when T' = 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. [2 marks]