7.9. Consider the model of a stock where it either goes up by 7% or down by 4% each year. Let Pup be the probability that stock goes up and pdown the probability that stock goes down. 1. Suppose that pup = 52% and pdown = 48%. Recall the expected rate of return i is defined as the number ji which satisfies the equation E[Si] = Sockxl where So is the known asset spot price and S, is the unknown asset price in one year from now. What is the expected rate of return of the stock? 2. If the risk-free rate is 5%, what probabilities Pup and pdown lead to an expected return equal to the risk-free rate? 7.10. Consider the example from the first part of) the previous example, where the spot price is So = $100. What is the probability that a 1-year butterfly made of European calls with strikes 90, 100 and 110 will have a payoff of $5 or less? 7.9. Consider the model of a stock where it either goes up by 7% or down by 4% each year. Let Pup be the probability that stock goes up and pdown the probability that stock goes down. 1. Suppose that pup = 52% and pdown = 48%. Recall the expected rate of return i is defined as the number ji which satisfies the equation E[Si] = Sockxl where So is the known asset spot price and S, is the unknown asset price in one year from now. What is the expected rate of return of the stock? 2. If the risk-free rate is 5%, what probabilities Pup and pdown lead to an expected return equal to the risk-free rate? 7.10. Consider the example from the first part of) the previous example, where the spot price is So = $100. What is the probability that a 1-year butterfly made of European calls with strikes 90, 100 and 110 will have a payoff of $5 or less