第一题：

Problem 2.
You are given the following information about a securities market:
i). There are two stocks, X and Y, which do not pay dividend.
ii) The current prices for X and Y are both $100.
iii) The continuously compounded risk-free interest rate is 10%.
iv) There are three possible states for the prices of X and Y one year from

State X Y 1 200 0 2 50 0 3 0 200

Let CX be the price of a European call option on X, and PY be the price of a European put option on Y. Both options expire in one year and have a strike price of $95. Calculate PY − CX

第二题：

Problem 3. Suppose that there are three periods: 0,1, and 2. We consider stocks A, B, and C. None of the three stocks pay any dividend.

In period 0, the price of stock A is S0a = 99.5, the price of stock B is S0b = 94, and the price of stock C is S0c = 106.5. The one-period risk-free rate in period 0 is denoted by r0.

In period 1, there are three states: “up”, “med”, and “down”. State “up” occurs with probability 0.4; State “med” occurs with probability 0.3; State “down” occurs with probability 0.3. The prices of the three stocks in period 1 is given by the following table.

“up” “med” “down”Sa 110 95 90Sb 100 95 85Sc 120 100 95

The one-period risk-free rate in period 1 r1 is 5%.
Let C(110) be the price of a European call option on stock A that expires in period 2 with the

strike price 110.

Let P(110) be the price of a European put option on stock A that expires in period 2 with the strike price 110.

a. Let mu, mm, and md be the stochastic discount factor in States “up”, “med”, and “down” in period 1. Calculate mu, mm, and md.

b. Solve for r0.
c. Calculate C (110) − P (110).