A stock that does not pay dividends trades for $25.
a. 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%?
b. 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%?
c. What position would you be willing to take on the option priced according to the data in a. given your expectations as stated in b?
d. What would be the replicating portfolio for the option when the volatility is 30% per annum?
e. 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?
The solution calculates the value of European call option using Binomial tree.