Goal: Find the no arbitrage options price for a European call option using a simplified stock model Stock model: The current spot price for a non-dividend-paying stock is S_0 = 24. In this simplified model, we assume that at the end of one month there are only two possible prices S_1 = 28 or S_1 = 20. We also assume that the probability of the stock price equaling 28 is P(S_1 = 28) = .75 and P(S_1 = 20) = .25.

European call option: We consider a European call option with strike price K = 23 and expiration in one month. Risk-free rate: Assume that the one-month risk-free rate is 1%. This is equivalent to an annualized 12% rate compounded monthly. If you borrow or loan $D, then after one month it is worth $D(1.01).

a.What are the possible payoffs of the European call option at expiration? Remember that there are only two possible stock prices: 28 and 20.

b.Consider a portfolio with A shares of stock and B dollars invested at the risk free rate. Both A and B are allowed to be fractions and may be positive or negative.Negative values correspond to shorting a stock or borrowing money. Write down formulas for the possible values of this portfolio in one month. Your answer will include the variables A and B as well as the numbers 20, 28, and 1.01.

c. Find the values of A and B that guarantee that the values of (a) and (b) are always equal to each other. Notice that the .75 number is irrelevant

d. What is the value today of a portfolio with A shares of stock and B dollars, using the values of A and B that you found in (c)?