. 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 is defined as the number which satisfies the equation E[S1] = S0e 1 where S0 is the known asset spot price and S1 is the unknown asset price in one year from now. What is the expected rate of return of the stock?(This is the reference part)

Question:

Consider the example from (the first part of) the previous example, where the spot price is S0 = $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?