We consider an example of constructing a synthetic safe asset with two risky assets. Suppose that there are two periods: 0, and 1. We consider stocks A and B. Neither of the two stocks pay any dividend.

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

In period 1, there are two states: up and down. State up occurs with probability 0.6; State down occurs with probability 0.4. The prices of the two stocks in period 1 is given by the following table.

The one-period risk-free rate in period 1 r1 is 5%.

up down

Sa. 110. 90

Sb. 100 85

Let C(100) be the price of a European call option on stock A that expires in period 2 with the strike price 100.

Let P(100) be the price of European put option on stock A that expires in period 2 with the strike price 100.

(a) Solve for r0 (5 points) (b) Calculate C(100) P (100) (5 points)