1. Consider the one-period Binomial market model. The savings account is $1 at time 0 and $8 at time 1. The stock price is given by So = 1 and S = where is a random variable taking two possible values u and d, each with positive probability. Moreover, assume that 0 Problem 4-2 (algorithmic) Question Help Vaniteux's Returns (A). Spencer Grant is a New York-based investor. He has been closely following his investment in 500 shares of Vaniteux, a French firm that went public in February 2010. When he purchased his 500 shares at 16.37 per share, the euro was trading at $1.3511/. Currently, the share is trading at 28.89 per share, and the dollar has fallen to $1.4143/E a. If Spencer sells his shares today, what percentage change in the share price would he receive? b. What is the percentage change in the value of the euro versus the dollar over this same period? c. What would be the total return Spencer would earn on his shares if he sold them at these rates? a. If Spencer sells his shares today, what percentage change in the share price would he receive? The shareholder return is %. (Round to two decimal places.) 4 rect: 0 Question 4. [30 marks] Suppose that in a particular discrete-time stock market, the stock prices follow a binomial tree model with the time step taken to be 1 year. Let u= 0.15 and d = -0.05 be the one-step rates of return of stock prices, corresponding to the price going up and down respectively. The current stock price S(0) = 50 and the risk-free rate of return for one year is r = 5%. (i) Find the risk-neutral probability of the binomial tree model. (ii) Find the risk-neutral expectation of the stock price EQ [S(2)] after two time steps. (iii) Suppose that the stock price goes up to 55 after one year. What is the risk-neutral conditional expectation of the stock price EQ [S(2)|S(1)]?