Question 2.

Suppose that the change in the price of a share of ABC stock is described by a multiplicative binomial lattice. There are three periods, period 0, period 1, and period 2. In period 0, the share price is S(0) = 180. At the beginning of each following period, the share price moves either up or down. The share price is multiplied by the factor u = 3/2 = 1.5 when there is an up move in the share price, and the share price is multiplied by the factor d = 2/3 = 0.6667 when there is a down move. Suppose also that the riskless interest rate is r = 0.10 that is 10 % per period.

1. Calculate the market value in period 0 of a European put option to sell one share of ABC stock with an exercise price of K = 150 that expires in period 1. Carefully explain your reasoning.
2. Consider a project whose payoffs are determined by the share price of ABC stock. In period 2, the project pays an amount 1250 if the price of a share of ABC stock in period 2 is 405, that is, if the share price has moved upward in both period 1 and period 2. The project also pays an amount 350 in period 2 if the price of a share of ABC stock in period 2 is 180, and the project pays an amount 280 in period 2 if the price of a share of ABC stock in period 2 is 80. For simplicity, suppose that there are no other costs or payoffs associated with the project. Calculate the market value of the project in period 0. Carefully explain your reasoning.
3. Explain how your estimate of the market value of the project described in section (ii) would change if the project also paid an amount 150 in period 1. Assume that the amount paid by the project in period 1 is the same whether the share price of ABC stock moves up or down in period 1.

Discuss how a change in (i) the time to expiration, T, (ii) the exercise price K, and (iii) the share price at the time of expiration, S(T), is likely to affect the market value of an American call option and an American put option to buy or sell one share of some stock. For the share price at the time of expiration, consider the value of the two options at the expiration date. For the time to expiration and the exercise price, consider the value of the options at some date before the expiration date

Question 2.

Suppose that the change in the price of a share of ABC stock is described by a multiplicative binomial lattice. There are three periods, period 0, period 1, and period 2. In period 0, the share price is S(0) = 180. At the beginning of each following period, the share price moves either up or down. The share price is multiplied by the factor u = 3/2 = 1.5 when there is an up move in the share price, and the share price is multiplied by the factor d = 2/3 = 0.6667 when there is a down move. Suppose also that the riskless interest rate is r = 0.10 that is 10 % per period.

1. Calculate the market value in period 0 of a European put option to sell one share of ABC stock with an exercise price of K = 150 that expires in period 1. Carefully explain your reasoning.
2. Consider a project whose payoffs are determined by the share price of ABC stock. In period 2, the project pays an amount 1250 if the price of a share of ABC stock in period 2 is 405, that is, if the share price has moved upward in both period 1 and period 2. The project also pays an amount 350 in period 2 if the price of a share of ABC stock in period 2 is 180, and the project pays an amount 280 in period 2 if the price of a share of ABC stock in period 2 is 80. For simplicity, suppose that there are no other costs or payoffs associated with the project. Calculate the market value of the project in period 0. Carefully explain your reasoning.
3. Explain how your estimate of the market value of the project described in section (ii) would change if the project also paid an amount 150 in period 1. Assume that the amount paid by the project in period 1 is the same whether the share price of ABC stock moves up or down in period 1.

Discuss how a change in (i) the time to expiration, T, (ii) the exercise price K, and (iii) the share price at the time of expiration, S(T), is likely to affect the market value of an American call option and an American put option to buy or sell one share of some stock. For the share price at the time of expiration, consider the value of the two options at the expiration date. For the time to expiration and the exercise price, consider the value of the options at some date before the expiration date part 2 solve it just