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Problem 3. The DoubleStep stock price is currently $79 per share. Over each of the next two six-month periods it is expected to go up

Problem 3. The DoubleStep stock price is currently $79 per share. Over each of the next two six-month periods it is expected to go up by 5% or down by 6%. All the options mentioned below are on this stock. The continuously-compounding risk-free interest rate is 4% per annum. (ONLY NEED ANSWER TO PART #4)

  1. What is the value of a one-year European call option that strikes at $80?
  2. What is the value of a one-year European put option that strikes at $80?
  3. Do the European call and put option values satisfy the put-call parity? Show your verification.
  4. If the put option were American, would it ever be optimal to exercise before maturity? What would be the value of the option?

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