You are given the following information on a European Call Option. The option matures in 10 weeks
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Question:
You are given the following information on a European Call Option. The option matures in 10 weeks and is at the money. The current stock price of the underlying stock is $75.00. Assume that the stock price can either go up by 20% or go down by 10% each period.The risk free rate is 5.0% per year.
Compute the following using a 2-period Binomial Model (so, each period is 5 weeks):
- Set up a replicating portfolio of the stock and a risk free bond.
- Clearly show the payoff for the Stock, Bond and the Call in both periods.
- Calculate the Number of Stocks and Bonds in both periods required to replicate the call.
- Using no Arbitrage, compute the price of the Call option (CBin) using this replicating portfolio.
- Compute the probability (implied) that the Option will be exercised.
- Compute the annualized standard deviation (sigma (B-S-M) of the stock's return (Sigma for B-S-M).
- Compute the Black-Scholes-Merton theoretical option price for the Call option (CBSM).
- Compute the price of a B-S-M Put option using Put-Call Parity
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