Problem: A stock that does not pay dividends trades for $25.
Question 1: What is the value of a European call option on the stock with 4 months to maturity, if the volatility of the stock is 30% per annum, the strike price is $28 and the riskless rate is 10%?
Question 2: What would be the value of the above option if you expected that the volatility of the underlying over the next 4 months would be 20%?
Question 3: What position would you be willing to take on the option priced according to the data in (1). given your expectations as stated in b?
Question 4: What would be the replicating portfolio for the option when the volatility is 30% per annum?
Question 5: Using put-call parity, compute the price of the corresponding European put if the volatility of the underlying is 30% per annum? What would be the value of the put option if it were American?