Two stocks S and Z are traded today at prices as indicated in the following table. In one year from now, the prices of these stocks may move to three states. The risk-free rate is 5 percent per year.

Security

Time 0

Year 1

Security

Time

Year 1

$128

$125

S

$99.40

$110

Z

$101.90

$106

$75

$92

  1. Compute the risk-neutral probabilities and state prices.
  2. A portfolio manager bought a call on S at a strike price of $105 and sold a put on Z at a strike price of $107. What is his net cash flow today? Compute the probability with which the call will be exercised. Compute the probability with which the put will be exercised.