Problem 2. Suppose that a stock has prices S(0) = $100 at time and S(T) is either 105 or 130 at time T 130 100 105 Letr be the one-period risk-free rate (For example, if $100 is invested into a bond at time 0, then the bonds value at time T is $100(1+r).) (1) Find the initial capital and the payoff of the following investment: 1. Invest the amount (0) = $100 into a bond at time 0. 2. Sell one share of stock at time 0. 3. Buy the stock at time T. 4. Sell the bonds of time T. (ii) Explain that if r> 1910000 = 0.3 then the investment in (1) is an arbitrage opportunity. (H) Show that either r 1900 = 0.05 or there is an arbitrage opportunity. Hint: you need to design a new investment similar to (i). (iv) Conclude from (ii). (ii) that if the No-Arbitrage Principle is used then 0.05 Sr 30.3. Problem 2. Suppose that a stock has prices S(0) = $100 at time 0 and S(T) is either 105 or 130 at time T. 130 100. 105 Letr be the one-period risk-free rate. (For example, if $100 is invested into a bond at time 0, then the bonds value at time T is $100(1+r).) (1) Find the initial capital and the payoff of the following investment: 1. Invest the amount S(0) = $100 into a bond at time 0. 2. Sell one share of stock at time 0. 3. Buy the stock at time T. 4. Sell the bonds at time T. (ii) Explain that ifr> 1900 = 0.3 then the investment in (1) is an arbitrage opportunity. (iii) Show that either r > 1091,00 = 0.05 or there is an arbitrage opportunity. Hint: you need to design a new investment similar to (i). (iv) Conclude from (ii)(iii) that if the No-Arbitrage Principle is used then 0.05 Sr 30.3