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solution

  1. You are given the following information on a Non-Dividend paying European Call option. The option matures in 0.5 years and has a strike price of $56. The current stock price of the underlying stock is $60.0. Assume that the stock can either go up by 25% or down by 15% per period. Set up a replicating portfolio of the stock and a risk-free bond and use a one-period binomial model. The risk-free rate is 3.0% per year:
  1. Clearly show the payoffs for the Stock, Bond and the Call.
  2. Calculate the Number of Stocks and Bonds required to replicate the call.
  3. Using no Arbitrage, compute the price of the Call option (CBin) using this replicating portfolio.
  4. Compute the probability that the option will be exercised.
  5. Compute the Black- Scholes- theoretical option price for a European Call option (CB-S-M) on the stock – Assume that the sigma or volatility for this equals 30% per year.
  6. Using Put –Call Parity, compute the price of a European Put option on a share of the stock.

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